| 000 | 01265camuuu200301 a 4500 | |
| 001 | 000000902848 | |
| 005 | 19990120165258.0 | |
| 008 | 830429s1984 ne a b 00110 eng | |
| 010 | ▼a 83009687 | |
| 020 | ▼a 9027712697 | |
| 040 | ▼a DLC ▼c DLC ▼d 244002 | |
| 041 | 1 | ▼a eng ▼h pol |
| 049 | 0 | ▼l 452027147 |
| 050 | 0 0 | ▼a QA171 ▼b .W3513 1984 |
| 082 | 0 0 | ▼a 512/.22 ▼2 19 |
| 090 | ▼a 512.22 ▼b W356gE | |
| 100 | 1 | ▼a Wawrzynczyk, Antoni. |
| 240 | 1 0 | ▼a Wspolczena teoria funkcji specjalnych. ▼l English |
| 245 | 1 0 | ▼a Group representations and special functions / ▼c Antoni Wawrzynczyk ; examples and problems prepared by Aleksander Strasburger. |
| 260 | ▼a Dordrecht ; ▼a Boston : ▼b D. Reidel ; ▼a Warszawa : ▼b PWN-Polish Scientific Publishers ; ▼a Hingham, MA, U.S.A. : ▼b Distributed for the U.S.A. and Canada, Kluwer Boston, ▼c c1984. | |
| 300 | ▼a xvi, 688 p. : ▼b ill. ; ▼c 23 cm. | |
| 490 | 1 | ▼a Mathematics and its applications. East European series. |
| 500 | ▼a Translation of: Wspolczesna teoria funkcji specjalnych. | |
| 504 | ▼a Includes bibliography(p. 672-679)and index. | |
| 650 | 0 | ▼a Representations of groups. |
| 650 | 0 | ▼a Functions, Special. |
| 700 | 1 | ▼a Strasburger, Aleksander. |
| 830 | 0 | ▼a Mathematics and its applications (D. Reidel Publishing Company). ▼p East European series. |
소장정보
| No. | 소장처 | 청구기호 | 등록번호 | 도서상태 | 반납예정일 | 예약 | 서비스 |
|---|---|---|---|---|---|---|---|
| No. 1 | 소장처 세종학술정보원/과학기술실/ | 청구기호 512.22 W356gE | 등록번호 452027147 | 도서상태 대출가능 | 반납예정일 | 예약 | 서비스 |
컨텐츠정보
목차
I.- 1. Groups and Homogeneous Spaces.- 1.1. Groups.- 1.2. Differentiate Manifolds.- 1.3. Lie Groups and Lie Algebras.- 1.4. Transformation Groups. Invariant Tensor Fields.- 1.5. Additional Structures on Manifolds.- 1.6. The Hurwitz Measure.- 1.7. Quasi-Invariant Measures.- 1.8. Elements of the Classification of Lie Groups and Algebras.- 2. Representations of Locally Compact Groups.- 2.1. Definition of a Representation. Examples.- 2.2. Basic Constructions. Induced Representations.- 2.3. Further Constructions of Representations.- 2.4. Intertwinning Operators. Unitary Equivalence of Representations.- 2.5. Positive Definite Measures and Cyclic Representations.- 2.6. Matrix Elements of Representations.- 2.7. Group Algebra Representations and Group Representations.- 2.8. The Universal Enveloping Algebra of a Lie Group Algebra. The Differential of a Representation.- 3. Decomposition Theory of Unitary Representations.- 3.1. Irreducible Representations. Schur's Lemma.- 3.2. Classical Fourier Transformation.- 3.3. The Fourier Transforms of Functions in D (Rn).- 3.4. Analysis on the Multiplicative Group R+. The Mellin Transformation.- 3.1. The Circle Group and the Fourier Series.- 3.2. Fourier Analysis on a Commutative Locally Compact Group.- 4. Representations of Compact Groups.- 4.1. Operators of the Hilbert-Schmidt Type.- 4.2. The Tensor Product of Hilbert Spaces.- 4.3. The Frobenius Theorem.- 4.4. The Peter-Weyl Theory.- 4.5. The Orthogonality Relations of Matrix Elements.- 4.6. Characters of Finite-Dimensional Representations.- 4.7. Harmonic Analysis on Compact Groups and on Their Homogeneous Spaces.- 5. Theory of Spherical Functions.- 5.1. The Spherical Integral Equation.- 5.2. Spherical Functions and Spherical Representations.- 5.3. Existence of Spherical Functions. Gelfand Pairs.- 5.4. Differentiability of Spherical Functions on Lie Groups.- II.- 6. The Euler ?- and B-Functions.- 6.1. Definition of the ?-Function.- 6.2. The Fourier Transformation and the Mellin Transformation.- 6.3. The Reflection Formula for the ?-Function.- 6.4. The Riemann ?-Function.- 7. Bessel Functions.- 7.1. The Group of Rigid Motions of R2.- 7.2. Spherical Representations of the Group M(2).- 7.3. Properties of the Bessel Functions.- 7.4. Harmonic Analysis on the Symmetric Space of the Motion Group M(2). The Fourier-Bessel Transformation.- 8. Theory of Jacobi and Legendre Polynomials.- 8.1. Representations of the Group SL(2, C) on a Space of Polynomials.- 8.2. Properties of the Representations Tl and Their Consequences.- 8.3. Integral Equations for the Functions Pjkl.- 8.4. The Differential of the Representation Tl. Recurrence and Differential Equations for the Functions Pmnl.- 8.5. Characters of Irreducible Representations and New Integral Formulas for Legendre Functions.- 8.6. Harmonic Analysis on the Group SU(2) and the Sphere S2.- 8.7. Decomposition of the Tensor Product of Representations Tl. The Clebsch-Gordan Coefficients.- 9. Gegenbauer Polynomials.- 9.1. Information about the Group SO(n) and the Homogeneous Space Sn-1.- 9.2. Spherical Representations of the Group SO(n).- 9.3. Gegenbauer's Equation and Basic Recurrences.- 9.4. Integral Formulas for the Gegenbauer Polynomials.- 9.5. A Mean Value Theorem for a Spherical Function.- 10. Jacobi and Legendre Functions.- 10.1. Structure of the Group SL(2, R) and Its Homogeneous Spaces.- 10.2. Induced Representations of the Group SL(2,R).- 10.3. Properties of the Representation U? and the Function Bmnl.- 10.4. Differentials of the Representations U?. Recurrence Relations. Irreducibility.- 10.5. Harmonic Analysis on the Disc SU(1, 1)/K.- Chapter11. Harmonic Analysis on the Lobatschevsky space.- 11.1. The Group SL(2, C). Induced Spherical Representations.- 11.2. On the Structure of the Lobatschevsky Space.- 11.3. The Spherical Fourier Transformation on ?.- 11.4. Decomposition into Plane Waves on ?.- 11.5. Differential Properties of Spherical Functions.- 11.6. The Gelfand-Graev Transformation.- 11.7. Irre
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