Equiconvergence for Laguerre function series

Krzysztof Stempak

Studia Mathematica (1996)

  • Volume: 118, Issue: 3, page 285-300
  • ISSN: 0039-3223

Abstract

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We prove an equiconvergence theorem for Laguerre expansions with partial sums related to partial sums of the (non-modified) Hankel transform. Combined with an equiconvergence theorem recently proved by Colzani, Crespi, Travaglini and Vignati this gives, via the Carleson-Hunt theorem, a.e. convergence results for partial sums of Laguerre function expansions.

How to cite

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Stempak, Krzysztof. "Equiconvergence for Laguerre function series." Studia Mathematica 118.3 (1996): 285-300. <http://eudml.org/doc/216279>.

@article{Stempak1996,
abstract = {We prove an equiconvergence theorem for Laguerre expansions with partial sums related to partial sums of the (non-modified) Hankel transform. Combined with an equiconvergence theorem recently proved by Colzani, Crespi, Travaglini and Vignati this gives, via the Carleson-Hunt theorem, a.e. convergence results for partial sums of Laguerre function expansions.},
author = {Stempak, Krzysztof},
journal = {Studia Mathematica},
keywords = {equiconvergence; Laguerre series; Hankel transform; equiconvergence theorem; Laguerre expansions},
language = {eng},
number = {3},
pages = {285-300},
title = {Equiconvergence for Laguerre function series},
url = {http://eudml.org/doc/216279},
volume = {118},
year = {1996},
}

TY - JOUR
AU - Stempak, Krzysztof
TI - Equiconvergence for Laguerre function series
JO - Studia Mathematica
PY - 1996
VL - 118
IS - 3
SP - 285
EP - 300
AB - We prove an equiconvergence theorem for Laguerre expansions with partial sums related to partial sums of the (non-modified) Hankel transform. Combined with an equiconvergence theorem recently proved by Colzani, Crespi, Travaglini and Vignati this gives, via the Carleson-Hunt theorem, a.e. convergence results for partial sums of Laguerre function expansions.
LA - eng
KW - equiconvergence; Laguerre series; Hankel transform; equiconvergence theorem; Laguerre expansions
UR - http://eudml.org/doc/216279
ER -

References

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  1. [CCTV] L. Colzani, A. Crespi, G. Travaglini and M. Vignati, Equiconvergence theorems for Fourier-Bessel expansions with applications to the harmonic analysis of radial functions in euclidean and noneuclidean spaces, Trans. Amer. Math. Soc. 338 (1993), 43-55. Zbl0785.42006
  2. [Ma] C. Markett, Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), 19-37. Zbl0515.42023
  3. [M1] B. Muckenhoupt, Mean convergence of Hermite and Laguerre series. II, Trans. Amer. Math. Soc. 147 (1970), 433-460. 
  4. [M2] B. Muckenhoupt, Equiconvergence and almost everywhere convergence of Hermite and Laguerre series, SIAM J. Math. Anal. 1 (1970), 295-321. Zbl0201.08501
  5. [St1] K. Stempak, On connections between Hankel, Laguerre and Heisenberg multipliers, J. London Math. Soc. 51 (1995), 286-298. Zbl0824.42004
  6. [St2] K. Stempak, Transplanting maximal inequalities between Laguerre and Hankel multipliers, Monatsh. Math., to appear. Zbl0866.42006
  7. [Sz] G. Szegö, Orthogonal Polynomials, Colloq. Publ. 23, Amer. Math. Soc., New York, 1939. 

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