Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications
نویسندگان
چکیده
منابع مشابه
Rational Ruijsenaars-schneider Hierarchy and Bispectral Difference Operators
Abstract. We show that a monic polynomial in a discrete variable n, with coefficients depending on time variables t1, t2, . . . is a τ -function for the discrete Kadomtsev-Petviashvili hierarchy if and only if the motion of its zeros is governed by a hierarchy of Ruijsenaars-Schneider systems. These τ -functions were considered in [10], where it was proved that they parametrize rank one solutio...
متن کاملLaguerre-type operators, Special functions and Applications
The monomiality principle was introduced (see e.g. [1] and the references therein) in order to derive properties of special polynomials from the corresponding ones holding for monomials. A set of paramount importance in this framework is given by the Hermite-Kampé de Fériet (shortly H-KdF) or Gould-Hopper polynomials [2], [3], [4]. As it is well known, the Hermite-Kampé de Fériet polynomials H ...
متن کاملEntire functions sharing a small entire function with their difference operators
In this paper, we mainly investigate the uniqueness of the entire function sharing a small entire function with its high difference operators. We obtain one results, which can give a negative answer to an uniqueness question relate to the Bruck conjecture dealt by Liu and Yang. Meanwhile, we also establish a difference analogue of the Bruck conjecture for entire functions of order less than 2, ...
متن کاملInequalities of Hardy-Littlewood-Polya Type for Functions of Operators and Their Applications
In this paper, we derive a generalized multiplicative Hardy-LittlewoodPolya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of a function of an operator on a class of elements defined with the help of another function of the operator. We then apply the results to solve the following p...
متن کاملExtended Jacobi and Laguerre Functions and their Applications
The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We prove some important properties of these operators such as: These sets of functions are orthogonal with respect to a positive de nite inner product de ned over the compact intervals [-1, 1] and [0,1), respectively and also th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2009
ISSN: 1815-0659
DOI: 10.3842/sigma.2009.054