Abstract
We study the algebra of functions on the set ℕ of natural numbers with respect to the generalized convolution, generated by the generalized translation operator Tnf(k)=f(max (n, k)), n, k∈ℕ. With the help of the generalized Fourier transform, connected with this convolution, we establish numerous identities and recurrence relations, connecting, in particular, sums of powers of natural numbers.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 372–377, March, 1990.
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Chernov, V.G. A certain functional algebra. Ukr Math J 42, 331–336 (1990). https://doi.org/10.1007/BF01057018
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DOI: https://doi.org/10.1007/BF01057018