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- W2075367979 abstract "In 1928 Hardy [1] proved that the class () is invariant under the -transformation of the Fourier coefficients. In 1944 Bellman [3] proved the dual result for the class () with respect to the adjoint transformation of the Fourier coefficients the transpose of the matrix of the -method.In the present paper a new proof of Bellman's theorem that does not depend on Hardy's theorem is given, and a representation of the function with the transformed Fourier series in terms of the original function, similar to the Hardy representation, is obtained. In addition an inaccuracy in the statement of the second half of Bellman's theorem is corrected. Finally, integral analogues of these results are proved. These analogues were derived on a heuristic level in the paper of Bellman without justifying the computations and without stating the conditions imposed on the functions.Bibliography: 18 titles." @default.
- W2075367979 created "2016-06-24" @default.
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- W2075367979 date "1995-02-28" @default.
- W2075367979 modified "2023-09-23" @default.
- W2075367979 title "ON A THEOREM OF BELLMAN ON FOURIER COEFFICIENTS" @default.
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- W2075367979 doi "https://doi.org/10.1070/sm1995v083n02abeh003593" @default.
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