Titlebook: Integral Geometry and Convolution Equations; V. V. Volchkov Book 2003 Springer Science+Business Media Dordrecht 2003 Fourier transform.con

只看該作者 · 發(fā)表于 2025-3-27 08:02:34

Behavior of Solutions of Convolution Equation at InfinityLet . ∈ .′(?.), . ≠ 0 and . ∈ ..(?.) be a nonzero function satisfying the equation . Then . cannot decrease rapidly on infinity. For instance, if . ? .(?.), from (3.1), (1.6.2) we have .. Since . is an entire function the set . is dense nowhere in ?.. As . is continuous we obtain . = 0.

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只看該作者 · 發(fā)表于 2025-3-27 13:48:27

Comments and Open ProblemsConvolution equations and related questions have been studied by many authors (see the survey [B31] containing an extensive bibliography, and also [N1], [V40], [V44], [V49]–[V51], [T3]).

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只看該作者 · 發(fā)表于 2025-3-28 05:45:21

Sets and Mappings. ∈ . with property .. If a set . is subset of . then we write . ? .. We write . = . if . ? . and . ? . Denote by ?, ≠ the negation for the symbols ∈,=, respectively. As usual 0 denotes the empty set. For arbitrary sets . we denote . . = {. ∈ .: . ? .}. If . is a finite set then card . denotes the number of elements of ..

只看該作者 · 發(fā)表于 2025-3-28 10:00:49

Distributionscalled a distribution on ., if for each compact set . ? . there exist a constants . > 0, . ∈ ?. such that . This means that if the sequence .. ∈ ., . = 1, 2,..., converges in . to the function . then <..> → <.> as . → + ∞.

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