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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Localization for Riesz means of Fourier expansions


Authors: Leonardo Colzani, Giacomo Gigante and Ana Vargas
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 42B08; Secondary 28A78
Published electronically: June 10, 2014
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Abstract: The classical Riemann localization principle states that if an integrable function of one variable vanishes in an open set, then its Fourier expansion converges to zero in this set. This principle does not immediately extend to several dimensions, and here we study the Hausdorff dimension of the sets of points where localization for Riesz means of Fourier expansions may fail.


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Leonardo Colzani
Affiliation: Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via R.Cozzi 53, 20125 Milano, Italia
Email: leonardo.colzani@unimib.it

Giacomo Gigante
Affiliation: Dipartimento di Ingegneria dell’Informazione e Metodi Matematici, Università di Bergamo, Viale Marconi 5, 24044 Dalmine (BG), Italia
Email: giacomo.gigante@unibg.it

Ana Vargas
Affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, España
Email: ana.vargas@uam.es

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06076-5
PII: S 0002-9947(2014)06076-5
Keywords: Sets of divergence, localization, Riesz means, Hausdorff dimension.
Received by editor(s): August 31, 2012
Published electronically: June 10, 2014
Additional Notes: The third author was partially supported by Grant MTM2010-16518, Ministerio de Economía y Competitividad, Spain.
Article copyright: © Copyright 2014 American Mathematical Society