Serving both as an introduction to the subject and as a reference, this book presents the
theory in elegant form and with modern concepts and notation. It covers the general theory …

Abstract CONTENTS Introduction Chapter I. Hadamard's criterion and the Painlevé property
Chapter II. Solution of the Hadamard problem in the four-dimensional Minkowski space § …

This survey article, written for the Encyclopedia of Mathematical Physics, 2nd edition, is
devoted to the remarkable family of operators introduced by Charles Dunkl and to their $ q …

There exists a generalized Hankel transform of order $\alpha\geq-1/2$ on $\mathbb {R} $,
which is based on the eigenfunctions of the Dunkl operator\[\qquad\quad\quad T_\alpha f …

We propose commuting set of matrix-valued difference operators in terms of the elliptic
Baxter–Belavin R-matrix in the fundamental representation of GL M. In the scalar case M= 1 …

The integrable quantum many-body systems associated with the classical root systems are
formulated in terms of the (trigonometric) Dunkl operators. We define the Dunkl operators by …

A bstract We systematically study the interesting relations between the quantum elliptic
Calogero-Moser system (eCM) and its generalization, and their corresponding …

This paper is an expanded and updated version of the preprint arxiv: math/0406499. It
includes a more detailed description of the basics of the theory of Cherednik and Hecke …

We define the Dunkl and Dunkl–Heckman operators in infinite number of variables and use
them to construct the quantum integrals of the Calogero–Moser–Sutherland (CMS) problems …

The quantum integrability of the generalized elliptic Ruijsenaars models is shown. These
models are mathematically related to the Macdonald operator and the Macdonald …