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Some Applications of Spaces of Entire Functions

Published online by Cambridge University Press:  20 November 2018

Louis De Branges
Louis De Branges*
Affiliation:
New York University Institute of Mathematical Sciences
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A Hilbert space, whose elements are entire functions, is of particular interest if it has these properties:

(H1) Whenever F(z) is in the space and has a non-real zero w, the function is in the space and has the same norm as F(z).

(H2) For each non-real number w, the linear functional defined on the space by F(z) —> F(w) is continuous.

(H3) Whenever F(z) is in the space, is in the space and has the same norm as F(z). If E(z) is an entire function satisfying

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 563 - 583
Copyright
Copyright © Canadian Mathematical Society 1963

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