Sidon sets and Riesz sets for some measure algebras on the disk

Olivier Gebuhrer; Alan Schwartz

Colloquium Mathematicae (1997)

  • Volume: 72, Issue: 2, page 269-279
  • ISSN: 0010-1354

Abstract

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Sidon sets for the disk polynomial measure algebra (the continuous disk polynomial hypergroup) are described completely in terms of classical Sidon sets for the circle; an analogue of the F. and M. Riesz theorem is also proved.

How to cite

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Gebuhrer, Olivier, and Schwartz, Alan. "Sidon sets and Riesz sets for some measure algebras on the disk." Colloquium Mathematicae 72.2 (1997): 269-279. <http://eudml.org/doc/210464>.

@article{Gebuhrer1997,
abstract = {Sidon sets for the disk polynomial measure algebra (the continuous disk polynomial hypergroup) are described completely in terms of classical Sidon sets for the circle; an analogue of the F. and M. Riesz theorem is also proved.},
author = {Gebuhrer, Olivier, Schwartz, Alan},
journal = {Colloquium Mathematicae},
keywords = {disk polynomials; bivariate polynomials; Riesz sets; hypergroups; Sidon sets; disk polynomial; F. and M. Riesz theorem; measure algebra},
language = {eng},
number = {2},
pages = {269-279},
title = {Sidon sets and Riesz sets for some measure algebras on the disk},
url = {http://eudml.org/doc/210464},
volume = {72},
year = {1997},
}

TY - JOUR
AU - Gebuhrer, Olivier
AU - Schwartz, Alan
TI - Sidon sets and Riesz sets for some measure algebras on the disk
JO - Colloquium Mathematicae
PY - 1997
VL - 72
IS - 2
SP - 269
EP - 279
AB - Sidon sets for the disk polynomial measure algebra (the continuous disk polynomial hypergroup) are described completely in terms of classical Sidon sets for the circle; an analogue of the F. and M. Riesz theorem is also proved.
LA - eng
KW - disk polynomials; bivariate polynomials; Riesz sets; hypergroups; Sidon sets; disk polynomial; F. and M. Riesz theorem; measure algebra
UR - http://eudml.org/doc/210464
ER -

References

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  2. [BG91] M. Bouhaik and L. Gallardo, A Mehler-Heine formula for disk polynomials, Indag. Math. 1 (1991), 9-18. Zbl0727.33003
  3. [BG92] M. Bouhaik and L. Gallardo, Un théorème limite central dans un hypergroupe bidimensionnel, Ann. Inst. H. Poincaré 28 (1992), 47-61. Zbl0748.60025
  4. [BH95] W. R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, de Gruyter Stud. Math. 20, de Gruyter, Berlin, New York, 1995. 
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  6. [CS95] W. C. Connett and A. L. Schwartz, Continuous 2-variable polynomial hypergroups, in: Applications of Hypergroups and Related Measure Algebras (Providence, R.I.), O. Gebuhrer, W. C. Connett and A. L. Schwartz (eds.), Contemp. Math. 183, Amer. Math. Soc., 1995, 89-109. Zbl0828.43006
  7. [Edw67] R. E. Edwards, Fourier Series, Vols. I, II, Holt, Rinehart and Winston, New York, 1967. 
  8. [HK93] H. Heyer and S. Koshi, Harmonic Analysis on the Disk Hypergroup, Mathematical Seminar Notes, Tokyo Metropolitan University, 1993. 
  9. [Kan76] Y. Kanjin, A convolution measure algebra on the unit disc, Tôhoku Math. J. (2) 28 (1976), 105-115. 
  10. [Kan85] Y. Kanjin, Banach algebra related to disk polynomials, ibid. 37 (1985), 395-404. 
  11. [Koo72] T. H. Koornwinder, The addition formula for Jacobi polynomials, II, the Laplace type integral representation and the product formula, Tech. Report TW 133/72, Mathematisch Centrum, Amsterdam, 1972. Zbl0247.33018
  12. [Koo78] T. H. Koornwinder, Positivity proofs for linearization and connection coefficients of orthogonal polynomials satisfying an addition formula, J. London Math. Soc. (2) 18 (1978), 101-114. Zbl0386.33009
  13. [Rud62] W. Rudin, Fourier Analysis on Groups, Interscience Publishers, 1962. 
  14. [Sze67] G. Szegő, Orthogonal Polynomials, 2nd ed., Colloq. Publ. 23, Amer. Math. Soc., Providence, R.I., 1967. 

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