Representation of Lie Groups and Special Functions : Simplest Lie Groups, Special Functions and Integral Transforms
Vilenkin , N. Ja.; Klimyk, A. U.
ISBN 10: 9401055661 ISBN 13: 9789401055666
Editore: Springer, 2012
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One service mathematici has rendered the 'Et moi, ...• si j'avait IU comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belong., on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense', Eric T. Bell able to do something with it. O. H eaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other pans and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'el;re of this series.
Contenuti: Series Editor's Preface. Preface. List of Special Symbols. 0: Introduction. 1: Elements of the Theory of Lie Groups and Lie Algebras. 2: Group Representations and Harmonic Analysis on Groups. 3: Commutative Groups and Elementary Functions. The Group of Linear Transformations of the Straight Line and the Gamma-Function. Hypergeometric Functions. 4: Representations of the Groups of Motions of Euclidean and Pseudo-Euclidean Planes, and Cylindrical Functions. 5: Representations of Groups of Third Order Triangular Matrices, the Confluent Hypergeometric Function and Related Polynomials and Functions. 6: Representations of the Groups SU (2), SU (1,1) and Related Special Functions: Legendre, Jacobi, Chebyshev Polynomials and Functions, Gegenbauer, Krawtchouk, Meixner Polynomials. 7: Representations of the Groups SU (1,1) and SL (2, R) in Mixed Bases. The Hypergeometric Function. 8: Clebsch-Gordan Coefficients, Racah Coefficients, and Special Functions. Bibliography. Subject Index.
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Titolo: Representation of Lie Groups and Special ...
Casa editrice: Springer
Data di pubblicazione: 2012
Legatura: Brossura
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Representation of Lie Groups and Special Functions (eng)
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Representation of Lie Groups and Special Functions
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ISBN 13: 9789401055666
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Kartoniert / Broschiert. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Series Editor s Preface. Preface. List of Special Symbols. 0: Introduction. 1: Elements of the Theory of Lie Groups and Lie Algebras. 2: Group Representations and Harmonic Analysis on Groups. 3: Commutative Groups and Elementary Functions. The Group of . Codice articolo 5832255
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Representation of Lie Groups and Special Functions: Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms (Mathematics and its Applications)
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Representation of Lie Groups and Special Functions
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ISBN 10: 9401055661
ISBN 13: 9789401055666
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -0: Introduction.- 1: Elements of the Theory of Lie Groups and Lie Algebras.- 1.0. Preliminary Information from Algebra, Topology, and Functional Analysis.- 1.1. Lie Groups and Lie Algebras.- 1.2. Homogeneous Spaces with Semisimple Groups of Motions.- 2: Group Representations and Harmonic Analysis on Groups.- 2.1. Representations of Lie Groups and Lie Algebras.- 2.2. Basic Concepts of the Theory of Representations.- 2.3. Harmonic Analysis on Groups and on Homogeneous Spaces.- 3: Commutative Groups and Elementary Functions. The Group of Linear Transformations of the Straight Line and the Gamma-Function. Hypergeometric Functions.- 3.1. Representations of One-Dimensional Commutative Lie Groups and Elementary Functions.- 3.2. The Groups SO(2) and R, Fourier Series and Integrals.- 3.3. Fourier Transform in the Complex Domain. Mellin and Laplace Transforms.- 3.4. Representations of the Group of Linear Transforms of the Straight Line and the Gamma-Function.- 3.5. Hypergeometric Functions and Their Properties.- 4: Representations of the Groups of Motions of Euclidean and Pseudo-Euclidean Planes, and Cylindrical Functions.- 4.1. Representations of the Group ISO(2) and Bessel Functions with Integral Index.- 4.2. Representations of the Group ISO(1,1), Macdonald and Hankel Functions.- 4.3. Functional Relations for Cylindrical Functions.- 4.4. Quasi-Regular Representations of the Groups ISO(2), ISO(1,1) and Integral Transforms.- 5: Representations of Groups of Third Order Triangular Matrices, the Confluent Hypergeometric Function, and Related Polynomials and Functions.- 5.1. Representations of the Group of Third Order Real Triangular Matrices.- 5.2. Functional Relations for Whittaker Functions.- 5.3. Functional Relations for the Confluent Hypergeometric Function and for Parabolic Cylinder Functions.- 5.4. Integrals Involving Whittaker Functions and Parabolic Cylinder Functions.- 5.5. Representations of the Group of Complex Third Order Triangular Matrices, Laguerre and Charlier Polynomials.- 6: Representations of the Groups SU(2), SU(1,1) and Related Special Functions: Legendre, Jacobi, Chebyshev Polynomials and Functions, Gegenbauer, Krawtchouk, Meixner Polynomials.- 6.1. The Groups SU(2) and SU(1,1).- 6.2. Finite Dimensional Irreducible Representations of the Groups GL(2,C) and SU(2).- 6.3. Matrix Elements of the Representations T of the Group SL(2, C) and Jacobi, Gegenbauer and Legendre Polynomials.- 6.4. Representations of the Group SU(1,1).- 6.5. Matrix Elements of Representations of SU(1, 1), Jacobi and Legendre Functions.- 6.6. Addition Theorems and Multiplication Formulas.- 6.7. Generating Functions and Recurrence Formulas.- 6.8. Matrix Elements of Representations of SU(2) and SU(1,1) as Functions of Column Index. Krawtchouk and Meixner Polynomials.- 6.9. Characters of Representations of SU(2) and Chebyshev Polynomials.- 6.10. Expansion of Functions on the Group SU(2).- 7: Representations of the Groups SU(1,1) and SL(2, ) in Mixed Bases. The Hypergeometric Function.- 7.1. The Realization of Representations T in the Space of Functions on the Straight Line.- 7.2. Calculation of the Kernels of Representations R .- 7.3. Functional Relations for the Hypergeometric Function.- 7.4. Special Functions Connected with the Hypergeometric Function.- 7.5. The Mellin Transform and Addition Formulas for the Hypergeometric Function.- 7.6. The Kernels K33( , ; ; g) and Hankel Functions.- 7.7. The Kernels Kij( , ; g), i j, and Special Functions.- 7.8. Harmonic Analysis on the Group SL(2, R) and Integral Transforms.- 8: Clebsch-GordanCoefficients, Racah Coefficients, and Special Functions.- 8.1. Clebsch-Gordan Coefficients of the Group SU(2).- 8.2. Properties of CGC's of the Group SU(2).- 8.3. CGC's, the Hypergeometric Function 3F2(.; 1) and Jacobi Polynomials.- 8.4. Racah Coefficients of SU(2) and the Hypergeometric Function 4F3(.; 1).- 8.5. Hahn and Racah Polynomials.- 8.6. Clebsch-Gorda. Codice articolo 9789401055666
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Representation of Lie Groups and Special Functions
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ISBN 10: 9401055661
ISBN 13: 9789401055666
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -One service mathematici has rendered the 'Et moi, . si j'avait IU comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belong., on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense', Eric T. Bell able to do something with it. O. H eaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other pans and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics . .'; 'One service logic has rendered com puter science . .'; 'One service category theory has rendered mathematics . .'. All arguably true. And all statements obtainable this way form part of the raison d'el;re of this series. 640 pp. Englisch. Codice articolo 9789401055666
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Representation of Lie Groups and Special Functions : Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms
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ISBN 10: 9401055661
ISBN 13: 9789401055666
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - One service mathematici has rendered the 'Et moi, . si j'avait IU comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belong., on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense', Eric T. Bell able to do something with it. O. H eaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other pans and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics . .'; 'One service logic has rendered com puter science . .'; 'One service category theory has rendered mathematics . .'. All arguably true. And all statements obtainable this way form part of the raison d'el;re of this series. Codice articolo 9789401055666
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