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Norm Convergence of Riesz-Bochner Means For Radial Functions

Published online by Cambridge University Press:  20 November 2018

G. V. Welland
G. V. Welland*
Affiliation:
University of Missouri-St. Louis, St. Louis, Missouri
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It is well known now that certain spherical methods in k (≧2) dimensions are rather poor for reconstructing a function from its Fourier transform. Consider a function f in L1(Rk), k ≧ 2,

and

where both integrals are integrals in Rk, the first over the whole space the second over the ball of radius R; x • y is the usual Euclidean inner product of x and y in Rk and \z\2 = z • z.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 1 , 01 February 1975 , pp. 176 - 185
Copyright
Copyright © Canadian Mathematical Society 1975

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