zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Generalized Fock spaces and Weyl commutation relations for the Dunkl kernel. (English) Zbl 1052.33014

Dunkl operators on d generalize the classical partial derivatives; they generate a commutative algebra of differential-difference operators. Due to the work of Dunkl, Opdam, de Jeu, Rösler and others, it is well-known that there exist associated Dunkl kernels and Dunkl transforms (generalizing the classical exponentials and Fourier tranform) as well as heat semigroups and Hermite polynomials.

In the paper under review, Fock spaces and the chaos transform associated with Dunkl operators are introduced. In particular, relations to Hermite functions and commutation relations between Dunkl and multiplication operators are studied (while these relations are partially known). These commutation relations in particular lead to Weyl commutation relations.


MSC:
33C99Hypergeometric functions
39A70Difference operators
46E99Linear function spaces and their duals
47B99Special classes of linear operators