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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Estimates for Fourier sums and eigenvalues of integral operators via multipliers on the sphere
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by T. Jordão and V. A. Menegatto PDF
Proc. Amer. Math. Soc. 144 (2016), 269-283 Request permission

Abstract:

We provide estimates for weighted Fourier sums of integrable functions defined on the sphere when the weights originate from a multiplier operator acting on the space where the function belongs. That implies refined estimates for weighted Fourier sums of integrable kernels on the sphere that satisfy an abstract Hölder condition based on a parameterized family of multiplier operators defining an approximate identity. This general estimation approach includes an important class of multiplier operators, namely, that defined by convolutions with zonal measures. The estimates are used to obtain decay rates for the eigenvalues of positive integral operators on $L^2(S^m)$ and generated by a kernel satisfying the Hölder condition based on multiplier operators on $L^2(S^m)$.
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Additional Information
  • T. Jordão
  • Affiliation: Departamento de Matemática, ICMC-USP - São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil
  • MR Author ID: 896956
  • Email: thsjordao@gmail.com
  • V. A. Menegatto
  • Affiliation: Departamento de Matemática, ICMC-USP - São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil
  • MR Author ID: 358330
  • ORCID: 0000-0002-4213-8759
  • Email: menegatt@icmc.usp.br
  • Received by editor(s): May 29, 2014
  • Received by editor(s) in revised form: December 18, 2014
  • Published electronically: July 8, 2015
  • Additional Notes: The authors were partially supported by FAPESP, grants $\#$ 2011/21300-7 and $\#$ 2014/06209-1
  • Communicated by: Walter Van Assche
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 269-283
  • MSC (2010): Primary 33C65, 41A17, 41A36, 41A60, 42A16; Secondary 45M05, 45C05, 42B10, 42A82
  • DOI: https://doi.org/10.1090/proc12716
  • MathSciNet review: 3415595