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Reciprocal Convergence Classes for Fourier Series and Integrals
Published online by Cambridge University Press: 20 November 2018
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The classical result of Plancherel for Fourier cosine transforms of functions f(x) of the class L2(0, ∞) states that (see (7) for references)
converges in mean square to a function g(x) which also belongs to L2(0, ∞), and furthermore
Some years ago in a series of papers (1; 2; 3) on summation formulae I showed that a similar symmetrical theory for narrower classes of functions and ordinary convergence of the integrals can also be developed.
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