On The Rate of a.e. Convergence by Convolution Type Means

Alexander M. Stokolos

On The Rate of a.e. Convergence by Convolution Type Means

Mathematical Sciences

Research output: Contribution to conference › Presentation

Abstract

The talk is based on joint work with Walter Trebels (TU Darmstadt). K.I. Oskolkov 1977 raised the problem, how the norm-smoothness of f(x) entails a certain rate of a.e. convergence of an approximation process Ttf(x) towards f(x) for t → 0+ . The purpose of this talk is to demonstrate nearly optimal results concerning the rate of almost everywhere convergence of the Gauss-Weierstrass, Abel-Poisson, and Bochner-Riesz means of the one-dimensional Fourier integral. A typical result for these means is the following: If the function f belongs to the Besov space Bs p,p, 1 < p < ∞, 0 < s < 1, then Tmtf(x) − f(x) = ox<.sub>(ts) a.e. as t → 0 +.

Original language	American English
State	Published - May 2011
Event	Kennesaw State University Approximation Theory and Harmonic Analysis Workshop - Kennesaw, GA Duration: May 1 2011 → …

Conference

Conference	Kennesaw State University Approximation Theory and Harmonic Analysis Workshop
Period	05/1/11 → …

Keywords

A.E. convergence
Convolution type means

DC Disciplines

Mathematics

Cite this

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title = "On The Rate of a.e. Convergence by Convolution Type Means",

abstract = " The talk is based on joint work with Walter Trebels (TU Darmstadt). K.I. Oskolkov 1977 raised the problem, how the norm-smoothness of f(x) entails a certain rate of a.e. convergence of an approximation process Ttf(x) towards f(x) for t → 0+ . The purpose of this talk is to demonstrate nearly optimal results concerning the rate of almost everywhere convergence of the Gauss-Weierstrass, Abel-Poisson, and Bochner-Riesz means of the one-dimensional Fourier integral. A typical result for these means is the following: If the function f belongs to the Besov space Bs p,p, 1 < p < ∞, 0 < s < 1, then Tmtf(x) − f(x) = ox<.sub>(ts) a.e. as t → 0 +.",

keywords = "A.E. convergence, Convolution type means",

author = "Stokolos, {Alexander M.}",

year = "2011",

month = may,

language = "American English",

note = "Kennesaw State University Approximation Theory and Harmonic Analysis Workshop ; Conference date: 01-05-2011",

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TY - CONF

T1 - On The Rate of a.e. Convergence by Convolution Type Means

AU - Stokolos, Alexander M.

PY - 2011/5

Y1 - 2011/5

N2 - The talk is based on joint work with Walter Trebels (TU Darmstadt). K.I. Oskolkov 1977 raised the problem, how the norm-smoothness of f(x) entails a certain rate of a.e. convergence of an approximation process Ttf(x) towards f(x) for t → 0+ . The purpose of this talk is to demonstrate nearly optimal results concerning the rate of almost everywhere convergence of the Gauss-Weierstrass, Abel-Poisson, and Bochner-Riesz means of the one-dimensional Fourier integral. A typical result for these means is the following: If the function f belongs to the Besov space Bs p,p, 1 < p < ∞, 0 < s < 1, then Tmtf(x) − f(x) = ox<.sub>(ts) a.e. as t → 0 +.

AB - The talk is based on joint work with Walter Trebels (TU Darmstadt). K.I. Oskolkov 1977 raised the problem, how the norm-smoothness of f(x) entails a certain rate of a.e. convergence of an approximation process Ttf(x) towards f(x) for t → 0+ . The purpose of this talk is to demonstrate nearly optimal results concerning the rate of almost everywhere convergence of the Gauss-Weierstrass, Abel-Poisson, and Bochner-Riesz means of the one-dimensional Fourier integral. A typical result for these means is the following: If the function f belongs to the Besov space Bs p,p, 1 < p < ∞, 0 < s < 1, then Tmtf(x) − f(x) = ox<.sub>(ts) a.e. as t → 0 +.

KW - A.E. convergence

KW - Convolution type means

M3 - Presentation

T2 - Kennesaw State University Approximation Theory and Harmonic Analysis Workshop

Y2 - 1 May 2011

ER -

On The Rate of a.e. Convergence by Convolution Type Means

Abstract

Conference

Keywords

DC Disciplines

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