A remark on the preceding note by Bochner. (Q2617093)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark on the preceding note by Bochner. |
scientific article |
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A remark on the preceding note by Bochner. (English)
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1934
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Modifikation des obigen \textit{Bochner}schen Satzes: \(f(x)\) sei meßbar. Wenn die Ungleichung \[ \left |\int _{-\infty }^\infty f(x)c(x)\,dx\right |\leq M\cdot \mathop{\operatorname{Max}}\limits _{-\infty <\alpha <\infty }\left |\int _{-\infty }^\infty e^{ix\alpha }c(x)\,dx\right | \] für alle \textit{Lebesgue}-integrierbaren Funktionen \(c(x)\) gilt, so besitzt \(f(x)\) eine Verteilungsfunktion \(V(\alpha )\) von beschränkter Schwankung mit Norm \(\leq M\).
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