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Norm Convergence of Riesz-Bochner Means For Radial Functions
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1975
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