Remarks on Orthogonal Polynomials and Balanced Realizations

Realizations of su ( 1 , 1 ) and U q ( su ( 1 , 1 ) ) and generating functions for orthogonal polynomials

Positive discrete series representations of the Lie algebra su(1, 1) and the quantum algebra U q (su(1, 1)) are considered. The diagonalization of a self-adjoint operator (the Hamiltonian) in these representations and in tensor products of such representations is determined , and the generalized eigenvectors are constructed in terms of orthogonal polynomials. Using simple realizations of su(1, ...

Some Remarks on a Paper by L. Carlitz

We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain Sobolev orthogonal polynomials.

Educational Article:Gramians and Balanced Realizations and their Application in System Order Reduction

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...

Remarks on Distance-Balanced Graphs

Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.