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A Bridge Between Lie Theory and Frame Theory : Applications of Lie Theory to Harmonic Analysis
| A Bridge Between Lie Theory and Frame Theory : Applications of Lie Theory to Harmonic Analysis |
| Autore | Oussa Vignon |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Newark : , : John Wiley & Sons, Incorporated, , 2025 |
| Descrizione fisica | 1 online resource (599 pages) |
| Disciplina | 512/.482 |
| Soggetto topico |
Frames (Vector analysis)
Lie groups Geometry, Differential Harmonic analysis |
| ISBN |
9781119712145
1119712149 9781119712169 1119712165 9781119712152 1119712157 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- Chapter 1 Introduction -- 1.1 Organization of the Book -- 1.2 Proficiency Expectations -- 1.3 Aims -- 1.4 Scope and Material Selection -- 1.5 Catering to Diverse Learning Approaches and Expertise Levels -- References -- Chapter 2 Differentiable Manifolds -- 2.1 Calculus on Euclidean Space -- 2.1.1 The Inverse Function Theorem and Its Applications -- 2.1.1.1 The Implicit Function and Constant Rank Theorems -- 2.2 Topological Manifolds -- 2.2.1 Differentiable Structures -- 2.2.2 Submanifolds -- 2.2.3 Derivations -- 2.2.4 Tangent Vectors -- 2.2.4.1 Tangent Vector As Equivalent Classes of Smooth Curves -- 2.2.4.2 Tangent Vectors As Derivations at a Point -- 2.2.5 Tangent Bundles -- 2.2.6 1‐Forms -- 2.2.7 Pull‐Backs -- 2.2.8 Tensor Fields -- References -- Chapter 3 Lie Theory -- 3.1 Lie Derivatives -- 3.2 Lie Groups and Lie Algebras -- 3.2.1 Lie Groups and Examples -- 3.2.2 Left and Right Translations -- 3.2.3 Lie Algebras -- 3.3 Exponential Map -- 3.4 Invariant Measure on Lie Groups -- 3.5 Homogeneous Spaces -- 3.6 Matrix Lie Theory -- 3.6.1 The Adjoint Maps -- 3.6.1.1 Lie's Theorem -- 3.7 Construction of Spline‐Type Partitions of Unity -- References -- Chapter 4 Representation Theory -- 4.1 Representations of Lie Groups and Lie Algebras -- 4.2 A Survey on the Theory of Direct Integrals -- 4.3 Induced Representations -- 4.3.1 Quasi‐invariant Measures on Cosets -- 4.3.2 Induced Unitary Characters -- 4.4 Integrability of Induced Characters -- References -- Chapter 5 Frame Theory -- 5.1 Series Expansions in Hilbert Spaces -- 5.2 Riesz Bases -- 5.3 Frames -- References -- Chapter 6 Frames on Euclidean Spaces -- 6.1 Wavelets and the ax+b Group -- 6.1.1 The Wavelet Representation -- 6.2 Gabor Systems and the Heisenberg Group -- References -- Chapter 7 Frames on Lie Groups.
7.1 Discretization of Induced Characters -- 7.1.1 Connection to Wavelet Theory and Time‐Frequency Analysis -- 7.1.2 A Toy Example -- 7.1.3 Proofs of Main Results -- 7.2 Localized Frames on Matrix Lie Groups -- 7.3 A Generalization -- References -- Chapter 8 Frames on Homogeneous Spaces -- 8.1 Localized Frames on Homogeneous Spaces -- 8.2 Frames on Spheres -- 8.3 Frames on the Klein Bottle -- References -- Chapter 9 Groups with Frames of Translates -- 9.1 Frames and Bases of Translates on the ax+b Lie Group -- References -- Chapter 10 Sampling and Interpolation on Unimodular Lie Groups -- 10.1 Admissible Representations -- 10.2 Gröchenig-Führ's Method of Oscillations -- 10.3 Sampling on Locally Compact Groups -- 10.4 Bandlimitation for Extensions of Rn -- 10.4.1 The Mautner Group and Its Relatives -- 10.4.2 Bandlimitation on a Class of Lie Groups -- 10.4.2.1 Spectral Analysis of Induced Representations -- References -- Chapter 11 Finite Frames Maximally Robust to Erasures -- 11.1 Inductive Construction of All Complex n‐Frames -- 11.2 Infinite Singly Generated Subgroups of Un -- 11.3 Random Sampling -- References -- Index -- EULA. |
| Record Nr. | UNINA-9911019626503321 |
Oussa Vignon
|
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| Newark : , : John Wiley & Sons, Incorporated, , 2025 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Finite frames : theory and applications / / Peter G. Casazza, Gitta Kutyniok, editors
| Finite frames : theory and applications / / Peter G. Casazza, Gitta Kutyniok, editors |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | [New York], : Birkhauser, c2013 |
| Descrizione fisica | 1 online resource (491 p.) |
| Disciplina | 515.733 |
| Altri autori (Persone) |
CasazzaPeter G
KutyniokGitta |
| Collana | Applied and numerical harmonic analysis |
| Soggetto topico | Frames (Vector analysis) |
| ISBN |
1-283-62171-1
9786613934161 0-8176-8373-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Constructing Finite Frames with a Given Spectrum.-Spanning and Independence Properties of Finite.-Alegebraic Geometry and Finite Frames -- Group Frames -- Gabor Framses in Finite Dimensions -- Frames as Codes -- Quantization and Finite Frames -- Finite Frames for Sparse Signal Processing -- Finite Frames and Filter Banks -- Finite Frame theory in Pure Mathematics -- Probabilitstic Frames -- Fusion Frames. |
| Record Nr. | UNINA-9910438154903321 |
| [New York], : Birkhauser, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / / Yeonhyang Kim [and three others], editors
| Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / / Yeonhyang Kim [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (xii, 343 pages) |
| Disciplina | 515/.63 |
| Collana | Contemporary Mathematics |
| Soggetto topico |
Frames (Vector analysis)
Harmonic analysis Wavelets (Mathematics) Gabor transforms Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Nontrigonometric harmonic analysis Information and communication, circuits -- Communication, information -- Communication, information Linear and multilinear algebra; matrix theory -- Basic linear algebra -- Basic linear algebra Operator theory -- General theory of linear operators -- General theory of linear operators Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Harmonic analysis in one variable Functional analysis -- Inner product spaces and their generalizations, Hilbert spaces -- Inner product spaces and their generalizations, Hilbert spaces Abstract harmonic analysis -- Abstract harmonic analysis -- Abstract harmonic analysis Approximations and expansions -- Approximations and expansions -- Approximations and expansions |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-4723-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910478950903321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / / Yeonhyang Kim [and three others], editors
| Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / / Yeonhyang Kim [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (xii, 343 pages) |
| Disciplina | 515/.63 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Frames (Vector analysis)
Harmonic analysis Wavelets (Mathematics) Gabor transforms Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Nontrigonometric harmonic analysis Information and communication, circuits -- Communication, information -- Communication, information Linear and multilinear algebra; matrix theory -- Basic linear algebra -- Basic linear algebra Operator theory -- General theory of linear operators -- General theory of linear operators Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Harmonic analysis in one variable Functional analysis -- Inner product spaces and their generalizations, Hilbert spaces -- Inner product spaces and their generalizations, Hilbert spaces Abstract harmonic analysis -- Abstract harmonic analysis -- Abstract harmonic analysis Approximations and expansions -- Approximations and expansions -- Approximations and expansions |
| ISBN | 1-4704-4723-1 |
| Classificazione | 15AXX41AXX42AXX42CXX43AXX46CXX47AXX94AXX |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910796857603321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / / Yeonhyang Kim [and three others], editors
| Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / / Yeonhyang Kim [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (xii, 343 pages) |
| Disciplina | 515/.63 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Frames (Vector analysis)
Harmonic analysis Wavelets (Mathematics) Gabor transforms Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Nontrigonometric harmonic analysis Information and communication, circuits -- Communication, information -- Communication, information Linear and multilinear algebra; matrix theory -- Basic linear algebra -- Basic linear algebra Operator theory -- General theory of linear operators -- General theory of linear operators Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Harmonic analysis in one variable Functional analysis -- Inner product spaces and their generalizations, Hilbert spaces -- Inner product spaces and their generalizations, Hilbert spaces Abstract harmonic analysis -- Abstract harmonic analysis -- Abstract harmonic analysis Approximations and expansions -- Approximations and expansions -- Approximations and expansions |
| ISBN | 1-4704-4723-1 |
| Classificazione | 15AXX41AXX42AXX42CXX43AXX46CXX47AXX94AXX |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910826297303321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Frames for undergraduates / Deguang Han ... [et al.]
| Frames for undergraduates / Deguang Han ... [et al.] |
| Pubbl/distr/stampa | Providence, R. I. : American Mathematical Society, c2007 |
| Descrizione fisica | xiv, 295 p. : ill. ; 22 cm |
| Disciplina | 515.63 |
| Altri autori (Persone) | Han, Deguangauthor |
| Collana | Student mathematical library, 1520-9121 ; 40 |
| Soggetto topico | Frames (Vector analysis) |
| ISBN |
9780821842126
0821842129 |
| Classificazione |
AMS 15-XX
LC QA433.F73 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991003809289707536 |
| Providence, R. I. : American Mathematical Society, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Frames, bases, and group representations / / Deguang Han, David R. Larson
| Frames, bases, and group representations / / Deguang Han, David R. Larson |
| Autore | Han Deguang <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2000 |
| Descrizione fisica | 1 online resource (111 p.) |
| Disciplina |
510 s
515/.63 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Frames (Vector analysis)
Operator theory Wavelets (Mathematics) Representations of groups |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0288-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Introduction""; ""Chapter 1. Basic Theory for Frames""; ""1.1. A Dilation Viewpoint on Frames""; ""1.2. The Canonical Dual Frame""; ""1.3. Alternate Dual Frames""; ""Chapter 2. Complementary Frames and Disjointness""; ""2.1. Strong Disjointness, Disjointness and Weak Disjointness""; ""2.2. Characterizations of Equivalence and Disjointness""; ""2.3. Cuntz Algebra Generators""; ""2.4. More on Alternate Duals""; ""Chapter 3. Frame Vectors for Unitary Systems""; ""3.1. The Local Commutant and Frame Vectors""; ""3.2. Dilation Theorems for Frame Vectors""
""3.3. Equivalence Classes of Frame Vectors""""Chapter 4. Gabor Type Unitary Systems""; ""Chapter 5. Frame Wavelets, Super-wavelets and Frame Sets""; ""5.1. Frame Sets""; ""5.2. Super-wavelets""; ""5.3. A Characterization of Super-wavelets""; ""5.4. Some Frazier-Jawerth Frames""; ""5.5. MRA Super-wavelets""; ""5.6. Interpolation Theory""; ""Chapter 6. Frame Representations for Groups""; ""6.1. Basics""; ""6.2. Frame Multiplicity""; ""6.3. Parameterizations of Frame Vectors""; ""6.4. Disjoint Group Representations""; ""Chapter 7. Concluding Remarks""; ""7.1. Spectral families of frames:"" ""7.2. A Joint Project with Pete Casazza""""7.3. A Matrix Completion Characterization of Frames""; ""7.4. Some Acknowledgements""; ""7.5. Density and Connectivity of Gabor Type Frames""; ""Bibliography"" |
| Record Nr. | UNINA-9910480869903321 |
|
Han Deguang <1959->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Frames, bases, and group representations / / Deguang Han, David R. Larson
| Frames, bases, and group representations / / Deguang Han, David R. Larson |
| Autore | Han Deguang <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2000 |
| Descrizione fisica | 1 online resource (111 p.) |
| Disciplina |
510 s
515/.63 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Frames (Vector analysis)
Operator theory Wavelets (Mathematics) Representations of groups |
| ISBN | 1-4704-0288-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Introduction""; ""Chapter 1. Basic Theory for Frames""; ""1.1. A Dilation Viewpoint on Frames""; ""1.2. The Canonical Dual Frame""; ""1.3. Alternate Dual Frames""; ""Chapter 2. Complementary Frames and Disjointness""; ""2.1. Strong Disjointness, Disjointness and Weak Disjointness""; ""2.2. Characterizations of Equivalence and Disjointness""; ""2.3. Cuntz Algebra Generators""; ""2.4. More on Alternate Duals""; ""Chapter 3. Frame Vectors for Unitary Systems""; ""3.1. The Local Commutant and Frame Vectors""; ""3.2. Dilation Theorems for Frame Vectors""
""3.3. Equivalence Classes of Frame Vectors""""Chapter 4. Gabor Type Unitary Systems""; ""Chapter 5. Frame Wavelets, Super-wavelets and Frame Sets""; ""5.1. Frame Sets""; ""5.2. Super-wavelets""; ""5.3. A Characterization of Super-wavelets""; ""5.4. Some Frazier-Jawerth Frames""; ""5.5. MRA Super-wavelets""; ""5.6. Interpolation Theory""; ""Chapter 6. Frame Representations for Groups""; ""6.1. Basics""; ""6.2. Frame Multiplicity""; ""6.3. Parameterizations of Frame Vectors""; ""6.4. Disjoint Group Representations""; ""Chapter 7. Concluding Remarks""; ""7.1. Spectral families of frames:"" ""7.2. A Joint Project with Pete Casazza""""7.3. A Matrix Completion Characterization of Frames""; ""7.4. Some Acknowledgements""; ""7.5. Density and Connectivity of Gabor Type Frames""; ""Bibliography"" |
| Record Nr. | UNINA-9910788841603321 |
|
Han Deguang <1959->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Frames, bases, and group representations / / Deguang Han, David R. Larson
| Frames, bases, and group representations / / Deguang Han, David R. Larson |
| Autore | Han Deguang <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2000 |
| Descrizione fisica | 1 online resource (111 p.) |
| Disciplina |
510 s
515/.63 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Frames (Vector analysis)
Operator theory Wavelets (Mathematics) Representations of groups |
| ISBN | 1-4704-0288-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Introduction""; ""Chapter 1. Basic Theory for Frames""; ""1.1. A Dilation Viewpoint on Frames""; ""1.2. The Canonical Dual Frame""; ""1.3. Alternate Dual Frames""; ""Chapter 2. Complementary Frames and Disjointness""; ""2.1. Strong Disjointness, Disjointness and Weak Disjointness""; ""2.2. Characterizations of Equivalence and Disjointness""; ""2.3. Cuntz Algebra Generators""; ""2.4. More on Alternate Duals""; ""Chapter 3. Frame Vectors for Unitary Systems""; ""3.1. The Local Commutant and Frame Vectors""; ""3.2. Dilation Theorems for Frame Vectors""
""3.3. Equivalence Classes of Frame Vectors""""Chapter 4. Gabor Type Unitary Systems""; ""Chapter 5. Frame Wavelets, Super-wavelets and Frame Sets""; ""5.1. Frame Sets""; ""5.2. Super-wavelets""; ""5.3. A Characterization of Super-wavelets""; ""5.4. Some Frazier-Jawerth Frames""; ""5.5. MRA Super-wavelets""; ""5.6. Interpolation Theory""; ""Chapter 6. Frame Representations for Groups""; ""6.1. Basics""; ""6.2. Frame Multiplicity""; ""6.3. Parameterizations of Frame Vectors""; ""6.4. Disjoint Group Representations""; ""Chapter 7. Concluding Remarks""; ""7.1. Spectral families of frames:"" ""7.2. A Joint Project with Pete Casazza""""7.3. A Matrix Completion Characterization of Frames""; ""7.4. Some Acknowledgements""; ""7.5. Density and Connectivity of Gabor Type Frames""; ""Bibliography"" |
| Record Nr. | UNINA-9910812748303321 |
|
Han Deguang <1959->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Harmonic analysis and applications : in honor of John J. Benedetto / Christopher Heil, editor
| Harmonic analysis and applications : in honor of John J. Benedetto / Christopher Heil, editor |
| Pubbl/distr/stampa | Boston : Birkhäuser, c2006 |
| Descrizione fisica | xxviii, 374 p. : ill. ; 25 cm |
| Disciplina | 515.2433 |
| Altri autori (Persone) |
Heil, Christopherauthor
Benedetto, John |
| Collana | Applied and numerical harmonic analysis |
| Soggetto (Persona) | Benedetto, John |
| Soggetto topico |
Harmonic analysis
Time-series analysis Frames (Vector analysis) |
| ISBN | 0817637788 |
| Classificazione |
AMS 42-06
AMS 00B30 AMS 42C AMS 94A20 LC QA403.H216 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991002024119707536 |
| Boston : Birkhäuser, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
