Special Functions and Their Symmetries \ Postgraduate Course in Applied Analysis

Special Functions and Their Symmetries
Postgraduate Course in Applied Analysis

University of Leeds, School of Mathematics

Lecturers: Vadim Kuznetsov (Room 9.18h) and Vladimir Kisil (Room 8.18l)
Web page: http://maths.leeds.ac.uk/~kisilv/courses/special.html

Description: This course is suitable for postgraduate students in both applied and pure mathematics. It presents fundamentals of special functions theory and its applications in partial differential equations of mathematical physics. The course covers topics in harmonic, classical and functional analysis, and combinatorics. It consists of the two parts: the first part gives the classic analytical approach and the second links the theory with groups of symmetries. The main objective of the course is to learn how:

To print lecture notes use PostScript files of the first and the second parts. See Technical notes on viewing online materials.

    Part I Algebraic and analytic methods, The PDF version is recommended. Lecturer: Vadim Kuznetsov
    1. Gamma and Beta functions.

    2. Hypergeometric series.

    3. Orthogonal polynomials.

    4. Separation of variables and special functions.

    5. Integrable systems and special functions.

    Part II Algebraic and symmetry methods. The PDF version is recommended. Lecturer: Vladimir Kisil
    1. Groups and Homogeneous Spaces .

    2. Representation of Groups and Their Decompositions .

    3. Real Harmonic Analysis .

    4. Harmonic Analysis on Spheres .

    5. Hermit Polynomials, Heisenberg Group, and Segal-Bargmann Spaces .

Pre-requisites: Basic real and complex analysis, rudimentary algebra.


George E. Andrews, Richard Askey, and Ranjan Roy. Special functions. Cambridge University Press, Cambridge, 1999.

Willard Miller, Jr. Lie Theory and Special Functions. Academic Press, New York, 1968. Mathematics in Science and Engineering, Vol. 43.

N. Ja. Vilenkin. Special Functions and the Theory of Group Representations. American Mathematical Society, Providence, R. I., 1968. Translated from the Russian by V. N. Singh. Translations of Mathematical Monographs, Vol. 22.
Tecnical Notes:

File translated from TEX by TTH, version 3.13.
On 22 May 2003, 14:49.