# 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)
Transforms associated to square integrable group representations. II: Examples. (English) Zbl 0601.22001
We give examples of integral transforms defined through square integrable group representations, described in the first paper of this series [J. Math. Phys. 26, 2473-2479 (1985; Zbl 0571.22021)]. We focus on the Weyl and $''ax+b''$ groups and study their relevance in physics and applied mathematics.

##### MSC:
 22A10 Analysis on general topological groups 22E70 Applications of Lie groups to physics; explicit representations
Full Text:
##### References:
 [1] A. Grossmann , J. Morlet and T. Paul , Journ. Math. Phys. , t. 26 , 1985 , p. 2473 . MR 803788 | Zbl 0571.22021 · Zbl 0571.22021 · doi:10.1063/1.526761 [2] T. Paul , J. Math. Phys. , t. 25 , 1984 , p. 3252 . MR 761848 [3] P. Goupillaud , A. Grossmann and J. Morlet , Geoexploration , t. 23 , 1984 - 1985 , p. 85 . [4] A. Grossmann and T. Paul , Wave functions on subgroups of the group of affine canonical transformations . In : Resonances. Models and Phenonema . S. Albeverio, L. S. Ferreira and L. Streit, editors. Springer , Lecture Notes in Physics , Vol. 211 , 1984 , p. 128 . MR 777335 [5] T. Paul , Affine coherent states and the radial Schrödinger equation I. Radial harmonic oscillator and hydrogen atom, II Large N limit and III Affine Wigner functions , preprints, Luminy . Submitted to Annals of I. H. P. [6] I.M. Gelfand and M.A. Naimark , Dokl-Akad-Navk SSSR , t. 55 , 1954 , p. 570 . [6] E.W. Aslasken and J.R. Klauder , J. Math. Phys. , t. 9 , 1968 , p. 206 . Zbl 0162.58403 · Zbl 0162.58403 · doi:10.1063/1.1664570