Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


SIGMA:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Symmetry, Integrability and Geometry: Methods and Applications, 2013, Volume 9, 010, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2013.010 (Mi sigma793) 		 
This article is cited in 10 scientific papers (total in 10 papers)

The Clifford Deformation of the Hermite Semigroup

Henrik De Biea, Ben Ørstedb, Petr Sombergc, Vladimir Součekc

a Department of Mathematical Analysis, Ghent University, Galglaan 2, 9000 Gent, Belgium
b Department of Mathematical Sciences, University of Aarhus, Building 530, Ny Munkegade, DK 8000, Aarhus C, Denmark
c Mathematical Institute of Charles University, Sokolovská 83, 186 75 Praha, Czech Republic
Full-text PDF (474 kB) Citations (10)
References:
PDF
HTML
DOI: https://doi.org/10.3842/SIGMA.2013.010
Abstract: This paper is a continuation of the paper [De Bie H., Ørsted B., Somberg P., Souček V., Trans. Amer. Math. Soc. 364 (2012), 3875–3902], investigating a natural radial deformation of the Fourier transform in the setting of Clifford analysis. At the same time, it gives extensions of many results obtained in [Ben Saïd S., Kobayashi T., Ørsted B., Compos. Math. 148 (2012), 1265–1336]. We establish the analogues of Bochner's formula and the Heisenberg uncertainty relation in the framework of the (holomorphic) Hermite semigroup, and also give a detailed analytic treatment of the series expansion of the associated integral transform.
Keywords: Dunkl operators; Clifford analysis; generalized Fourier transform; Laguerre polynomials; Kelvin transform; holomorphic semigroup.
Received: September 21, 2012; in final form January 29, 2013; Published online February 5, 2013
Bibliographic databases:
Document Type: Article
MSC: 33C52; 30G35; 43A32
Language: English
Citation: Henrik De Bie, Ben Ørsted, Petr Somberg, Vladimir Souček, “The Clifford Deformation of the Hermite Semigroup”, SIGMA, 9 (2013), 010, 22 pp.
Citation in format AMSBIB
\Bibitem{De OrsSom13}
\by Henrik~De Bie, Ben~{\O}rsted, Petr~Somberg, Vladimir~Sou{\v{c}}ek
\paper The Clifford Deformation of the Hermite Semigroup
\jour SIGMA
\yr 2013
\vol 9
\papernumber 010
\totalpages 22
\mathnet{http://mi.mathnet.ru/sigma793}
\crossref{https://doi.org/10.3842/SIGMA.2013.010}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3033552}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000314455200001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84873660187}
Linking options:
  • https://www.mathnet.ru/eng/sigma793
  • https://www.mathnet.ru/eng/sigma/v9/p10
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:216
    Full-text PDF :39
    References:38
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024