Rate of decay of convolution vs. frequency of sign changes (Q2772792)
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scientific article; zbMATH DE number 1708231
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rate of decay of convolution vs. frequency of sign changes |
scientific article; zbMATH DE number 1708231 |
Statements
2001
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decay of Poisson integral functions of exponential type
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sign changes
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0.81081307
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0.8036481
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0.79609513
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0.7920649
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Rate of decay of convolution vs. frequency of sign changes (English)
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Verbally the author points out how a previous result of himself [Expo. Math. 13, 247-275 (1995; Zbl 0835.31002)] can be used to get some new results on the sign changes for \(f\), if NEWLINE\[NEWLINEF(y)= O(e^{-ay})\quad\text{as }y\to \inftyNEWLINE\]NEWLINE and NEWLINE\[NEWLINEF(y)= {2\over\pi} \int^\infty_0 {y\over x^2+ y^2} f(x) dx,\quad y> 0.NEWLINE\]NEWLINE The original problem is due to B. F. Logan.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00019].
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