zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
The continuous wavelet transform and symmetric spaces. (English) Zbl 1033.42032
It is well known that the wavelet transform is related to a representation of the $ax+b$ group. The present paper concerns generalizations via a representation of a closed subgroup $H$ of $GL(n,\bbfR)$ on $\bbfR^n$. Under certain conditions such a representation leads to a decomposition of $L^2(\bbfR^n)$ into a finite number of irreducible representations, $L^2(\bbfR^n)= V_1 \oplus V_2 \oplus \cdots \oplus V_k$ (via the action of the semidirect product $H\times_s \bbfR^n$). The article focusses on the case where the stabilizer of a generic point in $\bbfR^n$ is a symmetric noncompact subgroup. In particular, it is proved that the generalized wavelet transform is invertible in this case.

42C40Wavelets and other special systems
43A85Analysis on homogeneous spaces
22E30Analysis on real and complex Lie groups
Full Text: DOI arXiv