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- W2093645158 abstract "Summary This paper contains results related to Titchmarsh's convolution theorem and valid for , the additive group of R n with the discrete topology. The method of proof consists in transferring the problem to R n with the usual topology by a procedure which has been used earlier, for instance in Helson [3]. In Section 1, the classical support theorems are generalized to . In [ 1 ], Titchmarsh's convolution theorem [ 6 ] on R was generalized to convolutions of functions belonging to certain weighted L p -spaces on R . Section 2 contains a corresponding generalization to weighted l 2 ( R d ). It should be observed that convolutions of elements f and g in l 1 ( ) can be interpreted as convolutions of bounded discrete measures on R n . Hence, in that case the support theorem (Theorem 4.33 of Hörmander [ 5 ]) is directly applicable to give the results of our Theorems 1 and 3. So the novelty in our theorems lies in the fact that they apply for instance to the case when it is only assumed f, g ∈ l 2 ( ), together with support conditions. It is not known whether it suffices to assume f ∈ l 1 ( ), g ∈ l p ( ), when p > 2." @default.
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- W2093645158 date "1989-10-01" @default.
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- W2093645158 title "Convolution theorems of Titchmarsh type on discrete Rn" @default.
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- W2093645158 doi "https://doi.org/10.1017/s0013091500004697" @default.
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