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Intrinsic Approach to Galois Theory of
| Intrinsic Approach to Galois Theory of |
| Autore | Vizio Lucia Di |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2022 |
| Descrizione fisica | 1 online resource (88 pages) |
| Disciplina |
515/.625
512.32 |
| Altri autori (Persone) | HardouinCharlotte |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Galois theory
Difference equations Difference and functional equations -- Difference equations -- Difference equations, scaling ($q$-differences) Field theory and polynomials -- Differential and difference algebra -- Difference algebra |
| ISBN |
9781470472306
1470472309 |
| Classificazione | 39A1312H10 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title page -- Introduction -- Grothendieck conjecture for -difference equations -- Intrinsic Galois groups -- Comparison with Malgrange-Granier Galois theory for non-linear differential equations -- Acknowledgments -- Part 1. Introduction to -difference equations -- Chapter 1. Generalities on -difference modules -- 1.1. Basic definitions -- 1.2. -difference modules, systems and equations -- 1.3. Some remarks on solutions -- 1.4. Trivial -difference modules -- Chapter 2. Formal classification of singularities -- 2.1. Regularity -- 2.2. Irregularity -- Part 2. Triviality of -difference equations with rational coefficients -- Chapter 3. Rationality of solutions, when is an algebraic number -- 3.1. The case of algebraic, not a root of unity -- 3.2. Global nilpotence. -- 3.3. Proof of Theorem 3.8 (and of Theorem 3.6) -- Chapter 4. Rationality of solutions when is transcendental -- 4.1. Statement of the main result -- 4.2. Regularity and triviality of the exponents -- 4.3. Proof of Theorem 4.2 -- 4.4. Link with iterative -difference equations -- Chapter 5. A unified statement -- Part 3. Intrinsic Galois groups -- Chapter 6. The intrinsic Galois group -- 6.1. Definition and first properties -- 6.2. Arithmetic characterization of the intrinsic Galois group -- 6.3. Finite intrinsic Galois groups -- 6.4. Intrinsic Galois group of a -difference module over \C( ), for ̸=0,1 -- Chapter 7. The parametrized intrinsic Galois group -- 7.1. Differential and difference algebra -- 7.2. Parametrized intrinsic Galois groups -- 7.3. Characterization of the parametrized intrinsic Galois group by curvatures -- 7.4. Parametrized intrinsic Galois group of a -difference module over \C( ), for ̸=0,1 -- 7.5. The example of the Jacobi Theta function -- Part 4. Comparison with the non-linear theory.
Chapter 8. Preface to Part 4. The Galois -groupoid of a -difference system, by Anne Granier -- 8.1. Definitions -- 8.2. A bound for the Galois -groupoid of a linear -difference system -- 8.3. Groups from the Galois -groupoid of a linear -difference system -- Chapter 9. Comparison of the parametrized intrinsic Galois group with the Galois -groupoid -- 9.1. The Kolchin closure of the Dynamics and the Malgrange-Granier groupoid -- 9.2. The groupoid \Gal{ ( )} -- 9.3. The Galois -groupoid \Galan{ ( )} vs the intrinsic parametrized Galois group -- 9.4. Comparison with known results -- Bibliography -- Back Cover. |
| Record Nr. | UNINA-9910955333303321 |
Vizio Lucia Di
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| Providence : , : American Mathematical Society, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari
| Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari |
| Autore | Jirari Alouf <1965-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1995 |
| Descrizione fisica | 1 online resource (154 p.) |
| Disciplina | 515/.625 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Sturm-Liouville equation
Difference equations Orthogonal polynomials |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0121-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""List of Figures""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""1.1 The Vibrating String""; ""1.2 Network Theory""; ""1.3 Random Walk With Discrete Time Process""; ""Chapter 2. Regular Sturm-Liouville Problem""; ""2.1 Set Up""; ""2.2 Preliminary Results""; ""2.3 Orthogonality, Eigenfunction Expansion, Spectral Function, and Green's Function""; ""Chapter 3. Singular Sturm-Liouville Problem""; ""3.1 Definition""; ""3.2 C[sub(b')] Circles""; ""3.3 C[sub(a')] Circles""; ""3.4 Existence of Boundary Conditions""; ""3.5 Singular Boundary Value Problems""
""3.6 Green's Function""""3.7 Self-Adjointness""; ""3.8 λ-Independence of Boundary Conditions""; ""3.9 Green's Formulas""; ""3.10 Spectral Resolution""; ""3.11 Limit-Point and Limit-Circle Tests""; ""Chapter 4. Polynomial Solutions""; ""4.1 Formal Self-Adjointness""; ""4.2 Polynomial Solutions""; ""4.3 Orthogonality of Eigenfunctions""; ""4.4 Eigenfunction Expansion""; ""Chapter 5. Polynomial Examples""; ""5.1 Classification""; ""5.2 Recurrence Relations""; ""5.3 Weight Functions and Self-Adjoint Forms""; ""5.4 Orthogonality""; ""5.5 Evaluation of the ||.||[sup(2)]""; ""5.6 Zeros"" ""Chapter 6. The Four Representative Examples""""6.1 The Generalized Tchebyshev Polynomials""; ""6.2 The Generalized Laguerre Polynomials""; ""6.3 The Krawtchouk Polynomials""; ""6.4 The Charlier Polynomials""; ""Chapter 7. Left-Definite Spaces""; ""7.1 Finite Intervals""; ""7.2 Infinite Intervals""; ""References"" |
| Record Nr. | UNINA-9910480338603321 |
|
Jirari Alouf <1965->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari
| Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari |
| Autore | Jirari Alouf <1965-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1995 |
| Descrizione fisica | 1 online resource (154 p.) |
| Disciplina | 515/.625 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Sturm-Liouville equation
Difference equations Orthogonal polynomials |
| ISBN | 1-4704-0121-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""List of Figures""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""1.1 The Vibrating String""; ""1.2 Network Theory""; ""1.3 Random Walk With Discrete Time Process""; ""Chapter 2. Regular Sturm-Liouville Problem""; ""2.1 Set Up""; ""2.2 Preliminary Results""; ""2.3 Orthogonality, Eigenfunction Expansion, Spectral Function, and Green's Function""; ""Chapter 3. Singular Sturm-Liouville Problem""; ""3.1 Definition""; ""3.2 C[sub(b')] Circles""; ""3.3 C[sub(a')] Circles""; ""3.4 Existence of Boundary Conditions""; ""3.5 Singular Boundary Value Problems""
""3.6 Green's Function""""3.7 Self-Adjointness""; ""3.8 λ-Independence of Boundary Conditions""; ""3.9 Green's Formulas""; ""3.10 Spectral Resolution""; ""3.11 Limit-Point and Limit-Circle Tests""; ""Chapter 4. Polynomial Solutions""; ""4.1 Formal Self-Adjointness""; ""4.2 Polynomial Solutions""; ""4.3 Orthogonality of Eigenfunctions""; ""4.4 Eigenfunction Expansion""; ""Chapter 5. Polynomial Examples""; ""5.1 Classification""; ""5.2 Recurrence Relations""; ""5.3 Weight Functions and Self-Adjoint Forms""; ""5.4 Orthogonality""; ""5.5 Evaluation of the ||.||[sup(2)]""; ""5.6 Zeros"" ""Chapter 6. The Four Representative Examples""""6.1 The Generalized Tchebyshev Polynomials""; ""6.2 The Generalized Laguerre Polynomials""; ""6.3 The Krawtchouk Polynomials""; ""6.4 The Charlier Polynomials""; ""Chapter 7. Left-Definite Spaces""; ""7.1 Finite Intervals""; ""7.2 Infinite Intervals""; ""References"" |
| Record Nr. | UNINA-9910788756103321 |
|
Jirari Alouf <1965->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari
| Second-order Sturm-Liouville difference equations and orthogonal polynomials / / Alouf Jirari |
| Autore | Jirari Alouf <1965-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1995 |
| Descrizione fisica | 1 online resource (154 p.) |
| Disciplina | 515/.625 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Sturm-Liouville equation
Difference equations Orthogonal polynomials |
| ISBN | 1-4704-0121-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""List of Figures""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""1.1 The Vibrating String""; ""1.2 Network Theory""; ""1.3 Random Walk With Discrete Time Process""; ""Chapter 2. Regular Sturm-Liouville Problem""; ""2.1 Set Up""; ""2.2 Preliminary Results""; ""2.3 Orthogonality, Eigenfunction Expansion, Spectral Function, and Green's Function""; ""Chapter 3. Singular Sturm-Liouville Problem""; ""3.1 Definition""; ""3.2 C[sub(b')] Circles""; ""3.3 C[sub(a')] Circles""; ""3.4 Existence of Boundary Conditions""; ""3.5 Singular Boundary Value Problems""
""3.6 Green's Function""""3.7 Self-Adjointness""; ""3.8 λ-Independence of Boundary Conditions""; ""3.9 Green's Formulas""; ""3.10 Spectral Resolution""; ""3.11 Limit-Point and Limit-Circle Tests""; ""Chapter 4. Polynomial Solutions""; ""4.1 Formal Self-Adjointness""; ""4.2 Polynomial Solutions""; ""4.3 Orthogonality of Eigenfunctions""; ""4.4 Eigenfunction Expansion""; ""Chapter 5. Polynomial Examples""; ""5.1 Classification""; ""5.2 Recurrence Relations""; ""5.3 Weight Functions and Self-Adjoint Forms""; ""5.4 Orthogonality""; ""5.5 Evaluation of the ||.||[sup(2)]""; ""5.6 Zeros"" ""Chapter 6. The Four Representative Examples""""6.1 The Generalized Tchebyshev Polynomials""; ""6.2 The Generalized Laguerre Polynomials""; ""6.3 The Krawtchouk Polynomials""; ""6.4 The Charlier Polynomials""; ""Chapter 7. Left-Definite Spaces""; ""7.1 Finite Intervals""; ""7.2 Infinite Intervals""; ""References"" |
| Record Nr. | UNINA-9910818934103321 |
|
Jirari Alouf <1965->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Some recent advances in partial difference equations / / editor, Eugenia Petropoulou
| Some recent advances in partial difference equations / / editor, Eugenia Petropoulou |
| Autore | Petropoulou Eugenia N |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | [S.l.], : Bentham e Books, [2010] |
| Descrizione fisica | 1 online resource (149 p.) |
| Disciplina |
515.625
515/.625 |
| Altri autori (Persone) | PetropoulouEugenia |
| Soggetto topico |
Difference equations
Difference algebra |
| ISBN |
9781608051526
1608051528 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 01 Title.pdf; 02 Cover Page; 03 eBooks End User License Agreement-Website; 04 Content; 06 Foreword; 07 Preface; 08 Chapter 01; 09 Chapter 02; 10 Chapter 03; 11 Chapter 04; 12 Index |
| Record Nr. | UNINA-9910970800903321 |
|
Petropoulou Eugenia N
|
||
| [S.l.], : Bentham e Books, [2010] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Some recent advances in partial difference equations [[electronic resource] /] / editor, Eugenia Petropoulou
| Some recent advances in partial difference equations [[electronic resource] /] / editor, Eugenia Petropoulou |
| Pubbl/distr/stampa | [S.l.], : Bentham e Books, [2010] |
| Descrizione fisica | 1 online resource (149 p.) |
| Disciplina |
515.625
515/.625 |
| Altri autori (Persone) | PetropoulouEugenia |
| Soggetto topico |
Difference equations
Difference algebra |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-60805-152-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 01 Title.pdf; 02 Cover Page; 03 eBooks End User License Agreement-Website; 04 Content; 06 Foreword; 07 Preface; 08 Chapter 01; 09 Chapter 02; 10 Chapter 03; 11 Chapter 04; 12 Index |
| Record Nr. | UNINA-9910459193603321 |
| [S.l.], : Bentham e Books, [2010] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Some recent advances in partial difference equations [[electronic resource] /] / editor, Eugenia Petropoulou
| Some recent advances in partial difference equations [[electronic resource] /] / editor, Eugenia Petropoulou |
| Pubbl/distr/stampa | [S.l.], : Bentham e Books, [2010] |
| Descrizione fisica | 1 online resource (149 p.) |
| Disciplina |
515.625
515/.625 |
| Altri autori (Persone) | PetropoulouEugenia |
| Soggetto topico |
Difference equations
Difference algebra |
| ISBN | 1-60805-152-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 01 Title.pdf; 02 Cover Page; 03 eBooks End User License Agreement-Website; 04 Content; 06 Foreword; 07 Preface; 08 Chapter 01; 09 Chapter 02; 10 Chapter 03; 11 Chapter 04; 12 Index |
| Record Nr. | UNINA-9910785305503321 |
| [S.l.], : Bentham e Books, [2010] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Symmetries and integrability of difference equations / edited by Decio Levi ... [et al.].
| Symmetries and integrability of difference equations / edited by Decio Levi ... [et al.]. |
| Pubbl/distr/stampa | Cambridge ; New York : Cambridge University Press, 2011 |
| Descrizione fisica | xviii, 341 p. : ill. ; 23 cm |
| Disciplina | 515/.625 |
| Altri autori (Persone) | Levi, Decio |
| Collana | London Mathematical Society lecture note series, 0076-0552 ; 381 |
| Soggetto topico |
Difference equations
Symmetry (Mathematics) Integrals |
| ISBN | 9780521136587 (pbk.) |
| Classificazione |
LC QA431
510.34 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Machine generated contents note: 1. Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals V. Dorodnitsyn and R. Kozlov; 2. Painleve; equations: continuous, discrete and ultradiscrete B. Grammaticos and A. Ramani; 3. Definitions and predictions of integrability for difference equations J. Hietarinta; 4. Orthogonal polynomials, their recursions, and functional equations M. E. H. Ismail; 5. Discrete Painleve; equations and orthogonal polynomials A. Its; 6. Generalized Lie symmetries for difference equations D. Levi and R. I. Yamilov; 7. Four lectures on discrete systems S. P. Novikov; 8. Lectures on moving frames P. J. Olver; 9. Lattices of compact semisimple Lie groups J. Patera; 10. Lectures on discrete differential geometry Yu. B Suris; 11. Symmetry preserving discretization of differential equations and Lie point symmetries of differential-difference equations P. Winternitz. |
| Record Nr. | UNISALENTO-991001417439707536 |
| Cambridge ; New York : Cambridge University Press, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Symmetries and integrability of difference equations / Decio Levi, Luc Vinet, Pavel Winternitz, editors
| Symmetries and integrability of difference equations / Decio Levi, Luc Vinet, Pavel Winternitz, editors |
| Pubbl/distr/stampa | Providence, R.I. : American Mathematical Society, c1996 |
| Descrizione fisica | xii, 388 p. : ill. ; 26 cm |
| Disciplina | 515/.625 |
| Altri autori (Persone) |
Levi, Decioauthor
Vinet, Lucauthor Winternitz, Pavelauthor |
| Altri autori (Convegni) | Workshop on Symmetries and Integrability of Difference Equations <1994 ; Estérel, Québec> |
| Collana | CRM Proceedings and Lecture Notes ; 1065-8580 ; v. 9 |
| Soggetto topico |
Difference equations - Congresses
Hypergeometric functions - Congresses Symmetry (Physics) - Congresses |
| ISBN | 0821806017 |
| Classificazione |
LC QA431
510.34 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991002037889707536 |
| Providence, R.I. : American Mathematical Society, c1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||