Some Applications of Spaces of Entire Functions
- 1 January 1963
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 15, 563-583
- https://doi.org/10.4153/cjm-1963-058-1
Abstract
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 satisfyingKeywords
This publication has 14 references indexed in Scilit:
- Symmetry in spaces of entire functionsDuke Mathematical Journal, 1962
- Homogeneous and periodic spaces of entire functionsDuke Mathematical Journal, 1962
- On fourier transforms of measures with compact supportActa Mathematica, 1962
- Some Hilbert spaces of entire functions. IIITransactions of the American Mathematical Society, 1961
- Some Hilbert spaces of entire functions. IITransactions of the American Mathematical Society, 1961
- The a-Local Operator ProblemCanadian Journal of Mathematics, 1959
- The Bernstein problemProceedings of the American Mathematical Society, 1959
- The Stone-Weierstrass theoremProceedings of the American Mathematical Society, 1959
- Local operators on Fourier transformsDuke Mathematical Journal, 1958
- Growth of analytic functions along a lineJournal d'Analyse Mathématique, 1954