On the estimation of Cesàro means of orthonormal series
J. Meder (1958)
Annales Polonici Mathematici
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J. Meder (1958)
Annales Polonici Mathematici
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Sundaram Thangavelu (1990)
Revista Matemática Iberoamericana
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C. G. G. Van Herk (1951)
Compositio Mathematica
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Gunther Schmidt (1995)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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The paper discusses new cubature formulas for classical integral operators of mathematical physics based on the «approximate approximation» of the density with Gaussian and related functions. We derive formulas for the cubature of harmonic, elastic and diffraction potentials approximating with high order in some range relevant for numerical computations. We prove error estimates and provide numerical results for the Newton potential.
Imre Z. Ruzsa, Andrzej Schinzel (1995)
Compositio Mathematica
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Ferenc Weisz (1998)
Studia Mathematica
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Elementary estimates for the Riesz kernel and for its derivative are given. Using these we show that the maximal operator of the Riesz means of a tempered distribution is bounded from to (1/(α+1) < p < ∞) and is of weak type (1,1), where is the classical Hardy space. As a consequence we deduce that the Riesz means of a function converge a.e. to ⨍. Moreover, we prove that the Riesz means are uniformly bounded on whenever 1/(α+1) < p < ∞. Thus, in case , the Riesz...
M. Gurdek, L. Rempulska, M. Skorupka (1999)
Collectanea Mathematica
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