Mathematics of the USSR-Sbornik · 1970 · 19 citations · 2 references
Natural SciencesPharmaceutical AnalysisAnalytic PhilosophyNumber TheoryRepresentation TheoryCharacteristic FunctionsOperator TheoryDirichlet Series
In the author's paper (On the representation of analytic functions by Dirichlet series, Math. USSR Sb. 9 (1969), 111-150) a theorem was proved stating that every function , analytic in a finite convex region and continuous in , can be represented in by a Dirichlet series. Here we have obtained a definitive result: any function , analytic in , is representable in by a Dirichlet series. The proof is based on the following assertion: let be a function analytic in a finite convex region . There exist a function , analytic in and continuous in , and an operator with characteristic function from the class , such that . Bibliography: 4 items.
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