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Embedding and multiplier theorems for H[superscript p](R[superscript n]) / / A. Baernstein II and E.T. Sawyer
| Embedding and multiplier theorems for H[superscript p](R[superscript n]) / / A. Baernstein II and E.T. Sawyer |
| Autore | Baernstein Albert, II, <1941-2014, > |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1985 |
| Descrizione fisica | 1 online resource (90 p.) |
| Disciplina | 515/.2433 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Hardy spaces
Embeddings (Mathematics) Multipliers (Mathematical analysis) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0731-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Introduction""; ""1. Embedding theorems""; ""2. Fourier embedding""; ""3. Multipliers""; ""4. Proof of Theorem 1""; ""5. Best possible nature of Theorems lb and lc""; ""6. Proof of Theorem 3""; ""7. Best possible nature of Theorems 3""; ""8. Lower majorant theorem""; ""9. On a theorem of Pigno and Smith""; ""10. Extension of a theorem of Oberlin""; ""References"" |
| Record Nr. | UNINA-9910480585703321 |
Baernstein Albert, II, <1941-2014, >
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1985 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Embedding and multiplier theorems for H[superscript p](R[superscript n]) / / A. Baernstein II and E.T. Sawyer
| Embedding and multiplier theorems for H[superscript p](R[superscript n]) / / A. Baernstein II and E.T. Sawyer |
| Autore | Baernstein Albert, II, <1941-2014, > |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1985 |
| Descrizione fisica | 1 online resource (90 p.) |
| Disciplina | 515/.2433 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Hardy spaces
Embeddings (Mathematics) Multipliers (Mathematical analysis) |
| ISBN | 1-4704-0731-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Introduction""; ""1. Embedding theorems""; ""2. Fourier embedding""; ""3. Multipliers""; ""4. Proof of Theorem 1""; ""5. Best possible nature of Theorems lb and lc""; ""6. Proof of Theorem 3""; ""7. Best possible nature of Theorems 3""; ""8. Lower majorant theorem""; ""9. On a theorem of Pigno and Smith""; ""10. Extension of a theorem of Oberlin""; ""References"" |
| Record Nr. | UNINA-9910788889603321 |
|
Baernstein Albert, II, <1941-2014, >
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1985 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Embedding and multiplier theorems for H[superscript p](R[superscript n]) / / A. Baernstein II and E.T. Sawyer
| Embedding and multiplier theorems for H[superscript p](R[superscript n]) / / A. Baernstein II and E.T. Sawyer |
| Autore | Baernstein Albert, II, <1941-2014, > |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1985 |
| Descrizione fisica | 1 online resource (90 p.) |
| Disciplina | 515/.2433 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Hardy spaces
Embeddings (Mathematics) Multipliers (Mathematical analysis) |
| ISBN | 1-4704-0731-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Introduction""; ""1. Embedding theorems""; ""2. Fourier embedding""; ""3. Multipliers""; ""4. Proof of Theorem 1""; ""5. Best possible nature of Theorems lb and lc""; ""6. Proof of Theorem 3""; ""7. Best possible nature of Theorems 3""; ""8. Lower majorant theorem""; ""9. On a theorem of Pigno and Smith""; ""10. Extension of a theorem of Oberlin""; ""References"" |
| Record Nr. | UNINA-9910819096903321 |
|
Baernstein Albert, II, <1941-2014, >
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1985 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Excursions in Harmonic Analysis, Volume 1 [[electronic resource] ] : The February Fourier Talks at the Norbert Wiener Center / / edited by Travis D Andrews, Radu Balan, John J. Benedetto, Wojciech Czaja, Kasso A. Okoudjou
| Excursions in Harmonic Analysis, Volume 1 [[electronic resource] ] : The February Fourier Talks at the Norbert Wiener Center / / edited by Travis D Andrews, Radu Balan, John J. Benedetto, Wojciech Czaja, Kasso A. Okoudjou |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | Boston, MA : , : Birkhäuser Boston : , : Imprint : Birkhäuser, , 2013 |
| Descrizione fisica | 1 online resource (488 p.) |
| Disciplina |
515.2433
515/.2433 |
| Collana | Applied and Numerical Harmonic Analysis |
| Soggetto topico |
Fourier analysis
Signal processing Image processing Speech processing systems Harmonic analysis Biomathematics Applied mathematics Engineering mathematics Fourier Analysis Signal, Image and Speech Processing Abstract Harmonic Analysis Mathematical and Computational Biology Mathematical and Computational Engineering Applications of Mathematics |
| ISBN |
1-283-94469-3
0-8176-8376-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part 1 Sampling Theory -- Unions of Subspaces for Data Modeling and Subspace Clustering -- Fusion frames and Unbiased Basic Sequences -- Sampling in Spaces of Bandlimited Functions on Commutative Spaces -- Smooth Interpolation of Data by Efficient Algorithms -- An Overview of Time and Multiband Limiting -- A Panorama of Sampling Theory -- Part II Remote Sensing -- Multistatic Radar Waveforms for Imaging of Moving Targets -- Exploitation Performance and Characterization of a Prototype Compressive Sensing Imaging Spectrometer -- An Introduction to Hyperspectral Image Data Modeling -- Hyperspectral Demixing: Sparse Recovery of Highly Correlated Endmembers -- Theory of Passive Synthetic Aperture Imaging -- Part III Mathematics of Data Processing -- Golay-Rudin-Shapiro Polynomials and Phased Arrays -- Multi-Resolution Geometric Analysis for Data in High Dimensions -- On the Fourth-Order Structure Function of a Fractal -- Harmonic Analysis of Databases and Matrices -- The Structure of Sidelobe-Preserving Operator Groups -- Zeros of some Self-Reciprocal Polynomials -- Part IV Applications of Data Processing -- Generalized Mutual Interdependence Analysis of Noisy Channels -- Approximation Methods for the Recovery of Shapes and Images from Gradients -- FM Perturbations due to Near-Identity Linear Systems -- Eddy Current Sensor Signal Processing for Stall Detection -- State Dependent Channels: Strong Converse and Bounds on Reliability Function. |
| Record Nr. | UNINA-9910437860703321 |
| Boston, MA : , : Birkhäuser Boston : , : Imprint : Birkhäuser, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Extensions of positive-definite distributions and maximum entropy / / Jean-Pierre Gabardo
| Extensions of positive-definite distributions and maximum entropy / / Jean-Pierre Gabardo |
| Autore | Gabardo Jean-Pierre <1958-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1993 |
| Descrizione fisica | 1 online resource (111 p.) |
| Disciplina | 515/.2433 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Fourier analysis
Positive-definite functions Maximum entropy method |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0066-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Abstract""; ""Introduction""; ""Notation""; ""1. The discrete case""; ""2. Positiveâ€?definite distributions on an interval (â€?A, A)""; ""3. The nonâ€?degenerate case""; ""4. A closure problem in L[sup(2)][sub(Î?)(R)""; ""5. Entropy maximizing measures in M [sub(A)](Q)""; ""6. Uniqueness of the extension""; ""References"" |
| Record Nr. | UNINA-9910480680903321 |
|
Gabardo Jean-Pierre <1958->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Extensions of positive-definite distributions and maximum entropy / / Jean-Pierre Gabardo
| Extensions of positive-definite distributions and maximum entropy / / Jean-Pierre Gabardo |
| Autore | Gabardo Jean-Pierre <1958-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1993 |
| Descrizione fisica | 1 online resource (111 p.) |
| Disciplina | 515/.2433 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Fourier analysis
Positive-definite functions Maximum entropy method |
| ISBN | 1-4704-0066-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Abstract""; ""Introduction""; ""Notation""; ""1. The discrete case""; ""2. Positiveâ€?definite distributions on an interval (â€?A, A)""; ""3. The nonâ€?degenerate case""; ""4. A closure problem in L[sup(2)][sub(Î?)(R)""; ""5. Entropy maximizing measures in M [sub(A)](Q)""; ""6. Uniqueness of the extension""; ""References"" |
| Record Nr. | UNINA-9910788879903321 |
|
Gabardo Jean-Pierre <1958->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Extensions of positive-definite distributions and maximum entropy / / Jean-Pierre Gabardo
| Extensions of positive-definite distributions and maximum entropy / / Jean-Pierre Gabardo |
| Autore | Gabardo Jean-Pierre <1958-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1993 |
| Descrizione fisica | 1 online resource (111 p.) |
| Disciplina | 515/.2433 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Fourier analysis
Positive-definite functions Maximum entropy method |
| ISBN | 1-4704-0066-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Abstract""; ""Introduction""; ""Notation""; ""1. The discrete case""; ""2. Positiveâ€?definite distributions on an interval (â€?A, A)""; ""3. The nonâ€?degenerate case""; ""4. A closure problem in L[sup(2)][sub(Î?)(R)""; ""5. Entropy maximizing measures in M [sub(A)](Q)""; ""6. Uniqueness of the extension""; ""References"" |
| Record Nr. | UNINA-9910817226403321 |
|
Gabardo Jean-Pierre <1958->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A first course in fourier analysis / / David W. Kammler [[electronic resource]]
| A first course in fourier analysis / / David W. Kammler [[electronic resource]] |
| Autore | Kammler David W. <1940-> |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2007 |
| Descrizione fisica | 1 online resource (1 volume (various pagings)) : digital, PDF file(s) |
| Disciplina | 515/.2433 |
| Soggetto topico | Fourier analysis |
| ISBN |
1-107-18586-6
1-281-24323-X 9786611243234 0-511-37780-0 0-511-37689-8 0-511-37595-6 0-511-37445-3 0-511-61970-7 0-511-37869-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | part 1. The mathematical core. Chapter 1. Fourier's representation for functions on R, Tp, Z, and PN. 1.1. Synthesis and analysis equations ; 1.2. Examples of Fourier's representation ; 1.3. The Parseval identities and related results ; 1.4. The Fourier-Poisson cube ; 1.5. The validity of Fourier's representation ; Chapter 2. Convolution of functions on R, Tp, Z, and PN. 2.1. Formal definitions of f * g, F x g ; 2.2. Computation of f * g ; 2.3. Mathematical properties of the convolution product ; 2.4. Examples of convolution and correlation ; Further reading ; Exercises ; Chapter 3. The calculus for finding Fourier transformations of functions on R. 3.1. Using the definition to find Fourier transformations ; 3.2. Rules for finding Fourier transformations ; 3.3. Selected applications of the Fourier transform calculus ; Further reading ; Exercises ; Chapter 4. The calculus for finding Fourier transforms of functions of Tp, Z, and PN. 4.1. Fourier series ; 4.2. Selected applications of Fourier series ; 4.3. Discrete Fourier transformations ; 4.4. Selected applications of the DFT calculus ; Further reading ; Exercises ; Chapter 5. Operator identities associated with Fourier analysis ; 5.1. the concept of an operator identity ; 5.2. Operators generated by powers of F ; 5.3. Operators related to complex conjugation ; 5.4. Fourier transforms of operators ; 5.5. Rules for Hartley transforms ; 5.6. Hilbert transforms ; Further reading ; Exercises ; Chapter 6. The fact Fourier transform. 6.1. Pre-FFT computation of the DFT ; 6.2. Deprivation of the FFT via DFT rules ; 6.3. The bit reversal permutation ; 6.4. Sparse matric factorization of F when N = 2m ; 6.5. Sparse matric factorization of H when N = 2m ; 6.6. Sparse matric factorization of F when N = P1P2...Pm ; 6.7. Kronecker product factorization of F ; Further reading ; Exercises ; Chapter 7. Generalized functions on R. 7.1. The concept of a generalized function ; 7.2. Common generalized functions ; 7.3. Manipulation of generalized functions ; 7.4. Derivatives and simple differential equations ; 7.5. The Fourier transform calculus for generalized functions ; 7.6. Limits of generalized functions ; 7.7. Periodic generalized functions ; 7.8. Alternative definitions for generalized functions ; Further reading ; Exercises -- Part 2. Selected applications. Chapter 8. Sampling. 8.1. Sampling and interpolation ; 8.2. Reconstruction of f from its samples ; 8.3. Reconstruction of f from samples of a1 * f, a2 * f, ... ; 8.4. Approximation of almost bandlimited functions ; Further reading ; Exercises ; Chapter 9. Partial differential equations. 9.1. Introduction ; 9.2. The wave equation ; 9.3. The diffusion equation ; 9.4. The diffraction equation ; 9.5. Fast computation of frames for movies ; Further reading ; Exercises ; Chapter 10. Wavelets. 10.1. The Haar wavelets ; 10.2. Support-limited wavelets ; 10.3. Analysis and synthesis with Daubechies wavelets ; 10.4. Filter banks ; Further reading ; Exercises ; Chapter 11. Musical tones. 11.1. Basic concepts ; 11.2. Spectrograms ; 11.3. Additive synthesis of tones ; 11.4. FM synthesis of tones ; 11.5. Synthesis of tones from noise ; 11.6. Music with mathematical structure ; Further reading ; Exercises ; Chapter 12. Probability. 12.1. Probability density functions of R ; 12.2. Some mathematical tools ; 12.3. The characteristic function ; 12.4. Random variables ; 12.5. The central limit theorem ; Further reading ; Exercises -- Appendices. Appendix 1. The impact of Fourier analysis ; Appendix 2. Functions and their Fourier transforms ; Appendix 3. The Fourier transform calculus ; Appendix 4. Operators and their Fourier transforms ; Appendix 5. The Whittaker-Robinson flow chart for harmonic analysis ; Appendix 6. FORTRAN code for a randix 2 FFT ; Appendix 7. The standard normal probability distribution ; Appendix 8. Frequencies of the piano keyboard. |
| Record Nr. | UNINA-9910451460203321 |
|
Kammler David W. <1940->
|
||
| Cambridge : , : Cambridge University Press, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A first course in fourier analysis / / David W. Kammler [[electronic resource]]
| A first course in fourier analysis / / David W. Kammler [[electronic resource]] |
| Autore | Kammler David W. <1940-> |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2007 |
| Descrizione fisica | 1 online resource (1 volume (various pagings)) : digital, PDF file(s) |
| Disciplina | 515/.2433 |
| Soggetto topico | Fourier analysis |
| ISBN |
1-107-18586-6
1-281-24323-X 9786611243234 0-511-37780-0 0-511-37689-8 0-511-37595-6 0-511-37445-3 0-511-61970-7 0-511-37869-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | part 1. The mathematical core. Chapter 1. Fourier's representation for functions on R, Tp, Z, and PN. 1.1. Synthesis and analysis equations ; 1.2. Examples of Fourier's representation ; 1.3. The Parseval identities and related results ; 1.4. The Fourier-Poisson cube ; 1.5. The validity of Fourier's representation ; Chapter 2. Convolution of functions on R, Tp, Z, and PN. 2.1. Formal definitions of f * g, F x g ; 2.2. Computation of f * g ; 2.3. Mathematical properties of the convolution product ; 2.4. Examples of convolution and correlation ; Further reading ; Exercises ; Chapter 3. The calculus for finding Fourier transformations of functions on R. 3.1. Using the definition to find Fourier transformations ; 3.2. Rules for finding Fourier transformations ; 3.3. Selected applications of the Fourier transform calculus ; Further reading ; Exercises ; Chapter 4. The calculus for finding Fourier transforms of functions of Tp, Z, and PN. 4.1. Fourier series ; 4.2. Selected applications of Fourier series ; 4.3. Discrete Fourier transformations ; 4.4. Selected applications of the DFT calculus ; Further reading ; Exercises ; Chapter 5. Operator identities associated with Fourier analysis ; 5.1. the concept of an operator identity ; 5.2. Operators generated by powers of F ; 5.3. Operators related to complex conjugation ; 5.4. Fourier transforms of operators ; 5.5. Rules for Hartley transforms ; 5.6. Hilbert transforms ; Further reading ; Exercises ; Chapter 6. The fact Fourier transform. 6.1. Pre-FFT computation of the DFT ; 6.2. Deprivation of the FFT via DFT rules ; 6.3. The bit reversal permutation ; 6.4. Sparse matric factorization of F when N = 2m ; 6.5. Sparse matric factorization of H when N = 2m ; 6.6. Sparse matric factorization of F when N = P1P2...Pm ; 6.7. Kronecker product factorization of F ; Further reading ; Exercises ; Chapter 7. Generalized functions on R. 7.1. The concept of a generalized function ; 7.2. Common generalized functions ; 7.3. Manipulation of generalized functions ; 7.4. Derivatives and simple differential equations ; 7.5. The Fourier transform calculus for generalized functions ; 7.6. Limits of generalized functions ; 7.7. Periodic generalized functions ; 7.8. Alternative definitions for generalized functions ; Further reading ; Exercises -- Part 2. Selected applications. Chapter 8. Sampling. 8.1. Sampling and interpolation ; 8.2. Reconstruction of f from its samples ; 8.3. Reconstruction of f from samples of a1 * f, a2 * f, ... ; 8.4. Approximation of almost bandlimited functions ; Further reading ; Exercises ; Chapter 9. Partial differential equations. 9.1. Introduction ; 9.2. The wave equation ; 9.3. The diffusion equation ; 9.4. The diffraction equation ; 9.5. Fast computation of frames for movies ; Further reading ; Exercises ; Chapter 10. Wavelets. 10.1. The Haar wavelets ; 10.2. Support-limited wavelets ; 10.3. Analysis and synthesis with Daubechies wavelets ; 10.4. Filter banks ; Further reading ; Exercises ; Chapter 11. Musical tones. 11.1. Basic concepts ; 11.2. Spectrograms ; 11.3. Additive synthesis of tones ; 11.4. FM synthesis of tones ; 11.5. Synthesis of tones from noise ; 11.6. Music with mathematical structure ; Further reading ; Exercises ; Chapter 12. Probability. 12.1. Probability density functions of R ; 12.2. Some mathematical tools ; 12.3. The characteristic function ; 12.4. Random variables ; 12.5. The central limit theorem ; Further reading ; Exercises -- Appendices. Appendix 1. The impact of Fourier analysis ; Appendix 2. Functions and their Fourier transforms ; Appendix 3. The Fourier transform calculus ; Appendix 4. Operators and their Fourier transforms ; Appendix 5. The Whittaker-Robinson flow chart for harmonic analysis ; Appendix 6. FORTRAN code for a randix 2 FFT ; Appendix 7. The standard normal probability distribution ; Appendix 8. Frequencies of the piano keyboard. |
| Record Nr. | UNINA-9910777025603321 |
|
Kammler David W. <1940->
|
||
| Cambridge : , : Cambridge University Press, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A first course in fourier analysis / / David W. Kammler [[electronic resource]]
| A first course in fourier analysis / / David W. Kammler [[electronic resource]] |
| Autore | Kammler David W. <1940-> |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2007 |
| Descrizione fisica | 1 online resource (1 volume (various pagings)) : digital, PDF file(s) |
| Disciplina | 515/.2433 |
| Soggetto topico | Fourier analysis |
| ISBN |
1-107-18586-6
1-281-24323-X 9786611243234 0-511-37780-0 0-511-37689-8 0-511-37595-6 0-511-37445-3 0-511-61970-7 0-511-37869-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | part 1. The mathematical core. Chapter 1. Fourier's representation for functions on R, Tp, Z, and PN. 1.1. Synthesis and analysis equations ; 1.2. Examples of Fourier's representation ; 1.3. The Parseval identities and related results ; 1.4. The Fourier-Poisson cube ; 1.5. The validity of Fourier's representation ; Chapter 2. Convolution of functions on R, Tp, Z, and PN. 2.1. Formal definitions of f * g, F x g ; 2.2. Computation of f * g ; 2.3. Mathematical properties of the convolution product ; 2.4. Examples of convolution and correlation ; Further reading ; Exercises ; Chapter 3. The calculus for finding Fourier transformations of functions on R. 3.1. Using the definition to find Fourier transformations ; 3.2. Rules for finding Fourier transformations ; 3.3. Selected applications of the Fourier transform calculus ; Further reading ; Exercises ; Chapter 4. The calculus for finding Fourier transforms of functions of Tp, Z, and PN. 4.1. Fourier series ; 4.2. Selected applications of Fourier series ; 4.3. Discrete Fourier transformations ; 4.4. Selected applications of the DFT calculus ; Further reading ; Exercises ; Chapter 5. Operator identities associated with Fourier analysis ; 5.1. the concept of an operator identity ; 5.2. Operators generated by powers of F ; 5.3. Operators related to complex conjugation ; 5.4. Fourier transforms of operators ; 5.5. Rules for Hartley transforms ; 5.6. Hilbert transforms ; Further reading ; Exercises ; Chapter 6. The fact Fourier transform. 6.1. Pre-FFT computation of the DFT ; 6.2. Deprivation of the FFT via DFT rules ; 6.3. The bit reversal permutation ; 6.4. Sparse matric factorization of F when N = 2m ; 6.5. Sparse matric factorization of H when N = 2m ; 6.6. Sparse matric factorization of F when N = P1P2...Pm ; 6.7. Kronecker product factorization of F ; Further reading ; Exercises ; Chapter 7. Generalized functions on R. 7.1. The concept of a generalized function ; 7.2. Common generalized functions ; 7.3. Manipulation of generalized functions ; 7.4. Derivatives and simple differential equations ; 7.5. The Fourier transform calculus for generalized functions ; 7.6. Limits of generalized functions ; 7.7. Periodic generalized functions ; 7.8. Alternative definitions for generalized functions ; Further reading ; Exercises -- Part 2. Selected applications. Chapter 8. Sampling. 8.1. Sampling and interpolation ; 8.2. Reconstruction of f from its samples ; 8.3. Reconstruction of f from samples of a1 * f, a2 * f, ... ; 8.4. Approximation of almost bandlimited functions ; Further reading ; Exercises ; Chapter 9. Partial differential equations. 9.1. Introduction ; 9.2. The wave equation ; 9.3. The diffusion equation ; 9.4. The diffraction equation ; 9.5. Fast computation of frames for movies ; Further reading ; Exercises ; Chapter 10. Wavelets. 10.1. The Haar wavelets ; 10.2. Support-limited wavelets ; 10.3. Analysis and synthesis with Daubechies wavelets ; 10.4. Filter banks ; Further reading ; Exercises ; Chapter 11. Musical tones. 11.1. Basic concepts ; 11.2. Spectrograms ; 11.3. Additive synthesis of tones ; 11.4. FM synthesis of tones ; 11.5. Synthesis of tones from noise ; 11.6. Music with mathematical structure ; Further reading ; Exercises ; Chapter 12. Probability. 12.1. Probability density functions of R ; 12.2. Some mathematical tools ; 12.3. The characteristic function ; 12.4. Random variables ; 12.5. The central limit theorem ; Further reading ; Exercises -- Appendices. Appendix 1. The impact of Fourier analysis ; Appendix 2. Functions and their Fourier transforms ; Appendix 3. The Fourier transform calculus ; Appendix 4. Operators and their Fourier transforms ; Appendix 5. The Whittaker-Robinson flow chart for harmonic analysis ; Appendix 6. FORTRAN code for a randix 2 FFT ; Appendix 7. The standard normal probability distribution ; Appendix 8. Frequencies of the piano keyboard. |
| Record Nr. | UNINA-9910825998203321 |
|
Kammler David W. <1940->
|
||
| Cambridge : , : Cambridge University Press, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
