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The a-Local Operator Problem

Published online by Cambridge University Press:  20 November 2018

Louis de Branges
Louis de Branges*
Affiliation:
Lafayette College
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Extract

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Let be the Fourier transform of a Borel measure of finite total variation. The formula

can be justified if the integral on the right converges absolutely. For

where

Now let h → 0 in both sides of this equation and use the Lebesgue dominated convergence theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 583 - 592
Copyright
Copyright © Canadian Mathematical Society 1959

References

1. Boas, R. P. Jr.,, Entire Functions (New York, 1954).Google Scholar
2. de Branges, L., Local Operators on Fourier Transforms, Duke Math. J. 25 (1958), 143-54.Google Scholar