Harmonic analysis on a locally compact hypergroup

Abstract

We propose a new axiomatics for a locally compact hypergroup. On the one hand, the new object generalizes a DJS-hypergroup and, on the other hand, it allows to obtain results similar to those for a unimodular hypecomplex system with continuous basis. We construct a harmonic analysis and, for a commutative locally compact hypergroup, give an analogue of the Pontryagin duality theorem.

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Article Information

Title	Harmonic analysis on a locally compact hypergroup
Source	Methods Funct. Anal. Topology, Vol. 16 (2010), no. 4, 304-332
MathSciNet	MR2777191
Copyright	The Author(s) 2010 (CC BY-SA)

Authors Information

A. A. Kalyuzhnyi
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

G. B. Podkolzin
National Technical University of Ukraine (KPI), 37, Prospect Peremogy, Kyiv, 03056, Ukraine

Yu. A. Chapovsky
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Citation Example

A. A. Kalyuzhnyi, G. B. Podkolzin, and Yu. A. Chapovsky, Harmonic analysis on a locally compact hypergroup, Methods Funct. Anal. Topology 16 (2010), no. 4, 304-332.

BibTex

@article {MFAT560,
    AUTHOR = {Kalyuzhnyi, A. A. and Podkolzin, G. B. and Chapovsky, Yu. A.},
     TITLE = {Harmonic analysis on a locally compact hypergroup},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {16},
      YEAR = {2010},
    NUMBER = {4},
     PAGES = {304-332},
      ISSN = {1029-3531},
  MRNUMBER = {MR2777191},
       URL = {http://mfat.imath.kiev.ua/article/?id=560},
}