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Group representations and special functions

Group representations and special functions (Loan 1 times)

Material type
단행본
Personal Author
Wawrzynczyk, Antoni. Strasburger, Aleksander.
Title Statement
Group representations and special functions / Antoni Wawrzynczyk ; examples and problems prepared by Aleksander Strasburger.
Publication, Distribution, etc
Dordrecht ;   Boston :   D. Reidel ;   Warszawa :   PWN-Polish Scientific Publishers ;   Hingham, MA, U.S.A. :   Distributed for the U.S.A. and Canada, Kluwer Boston,   c1984.  
Physical Medium
xvi, 688 p. : ill. ; 23 cm.
Series Statement
Mathematics and its applications. East European series.
ISBN
9027712697
General Note
Translation of: Wspolczesna teoria funkcji specjalnych.  
Bibliography, Etc. Note
Includes bibliography(p. 672-679)and index.
Subject Added Entry-Topical Term
Representations of groups. Functions, Special.
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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.

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Sejong Academic Information Center/Science & Technology/ Call Number 512.22 W356gE Accession No. 452027147 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents

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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