Fourier Transform of Unbounded Measures on Hypergroups

Massoud Amini

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 819-828
  • ISSN: 0392-4041

Abstract

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We show that an unbounded measure on a strong commutative hypergroup is transformable if and only if its convolution with any positive definite function of compact support is positive definite.

How to cite

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Amini, Massoud. "Fourier Transform of Unbounded Measures on Hypergroups." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 819-828. <http://eudml.org/doc/290373>.

@article{Amini2007,
abstract = {We show that an unbounded measure on a strong commutative hypergroup is transformable if and only if its convolution with any positive definite function of compact support is positive definite.},
author = {Amini, Massoud},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {819-828},
publisher = {Unione Matematica Italiana},
title = {Fourier Transform of Unbounded Measures on Hypergroups},
url = {http://eudml.org/doc/290373},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Amini, Massoud
TI - Fourier Transform of Unbounded Measures on Hypergroups
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 819
EP - 828
AB - We show that an unbounded measure on a strong commutative hypergroup is transformable if and only if its convolution with any positive definite function of compact support is positive definite.
LA - eng
UR - http://eudml.org/doc/290373
ER -

References

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  1. ARGABRIGHT, L. - DE LAMADRID, J., Fourier analysis of unbounded measures on locally compact abelian groups, Memoirs of the American Mathematical Society, No. 145, American Mathematical Society, Providence, R.I., 1974. Zbl0294.43002MR621876
  2. AMINI, M. - MEDGHALCHI, A., Fourier algebras on tensor hypergrups, Contemporary Math.363 (2004), 1-14. Zbl1061.43010MR2097946DOI10.1090/conm/363/06637
  3. BAAKE, M., Diffraction of weighted lattice subsets, Canad. Math. Bull.45, no. 4 (2002), 483-498. Zbl1161.52309MR1941223DOI10.4153/CMB-2002-050-2
  4. BLOOM, W. R., HEYER, H., Harmonic analysis of probability measures on hypergroups, de Gruyter Studies in Mathematics 20, Walter de Gruyter, Berlin, New York, 1995. Zbl0828.43005MR1312826DOI10.1515/9783110877595
  5. BOURBAKI, N., Elements de Mathematique, Integration, 2nd ed., Herman, Paris, 1965. MR209424
  6. EYMARD, P., L'algèbre de Fourier d'un groupe localement compact, Bull. Soc. Math. France92 (1964), 181-236. Zbl0169.46403MR228628
  7. GHAHRAMANI, F. - MEDGHALCHI, A. R., Compact multipliers on weighted hypergroup algebras I, II, Math. Proc. Camb. Phil. Soc.98 (1985), 493-500, 100 (1986), 145-149. Zbl0584.43004MR838661DOI10.1017/S0305004100065944
  8. JEWETT, R. I., Spaces with an abstract convolution of measures, Advances in Math.18 (1975), 1-110. MR394034DOI10.1016/0001-8708(75)90002-X
  9. RUDIN, W., Fourier analysis on groups, Wiley Classics Library, John Wiley and Sons, Inc., New York, 1990. Zbl0698.43001MR1038803DOI10.1002/9781118165621

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