Lecture notes on orthogonal polynomials of sev- eral variables

Lecture Notes on Orthogonal Polynomials of Several Variable

Orthogonal Polynomials TCU Seminar Lecture Notes

And a disclaimer: I've made lots of changes of variables throughout. Expect some mistakes. I would appreciate hearing about any you find. I want to look at two different topics that have to do with orthogonal polynomials. The first has to do with approximation; the second, with Mellin transforms and zeta functions. If we have an inner product on R[x], we can use Gram-Schmidt to convert {1, x, x...

Combinatorics of generalized Tchebycheff polynomials

By considering a family of orthogonal polynomials generalizing the Tchebycheff polynomials of the second kind we refine the corresponding results of De Sainte-Catherine and Viennot on Tchebycheff polynomials of the second kind (Lecture Notes in Mathematics, vol. 1171, 1985, Springer-Verlag, 120). © 2003 Elsevier Science Ltd. All rights reserved.

Dunkl Operators: Theory and Applications

These lecture notes are intended as an introduction to the theory of rational Dunkl operators and the associated special functions, with an emphasis on positivity and asymptotics. We start with an outline of the general concepts: Dunkl operators, the intertwining operator, the Dunkl kernel and the Dunkl transform. We point out the connection with integrable particle systems of Calogero-MoserSut...

Solving singular integral equations by using orthogonal polynomials

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...