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A generalization of lebesgue’s convergence criterion for fourier series

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For generalized Dirichlet integrals of type \(\int_0^1\ f(x)(e^{irx}-e^{airx}){dx\over x}\) a somewhat sharpened version of Lebesgue’s well-known convergence criterion for Fourier series is proven. Integrals of this type are of importance in the general theory of eigenfunction expansions inaugurated by investigations of Birkhoff, Tamarkin, and Stone.

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  1. Lehrstuhl I für Mathematik RWTH Aachen, (Technological University Aachen), gustinerbach 2a, D-5100, Aachen Fed. Rep, Germany

    Edgar M. E. Wermuth

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  1. Edgar M. E. Wermuth
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Wermuth, E.M.E. A generalization of lebesgue’s convergence criterion for fourier series. Results. Math. 15, 186–195 (1989). https://doi.org/10.1007/BF03322455

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