Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T05:40:02.877Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

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

References

1. Beurling, A. and Malliavin, P., On Fourier transforms of measures with compact support, Acta. Math., 107 (1962), 291–309.Google Scholar
2. Boas, R. P. Jr. , Entire functions (New York, 1954).Google Scholar
3. Boas, R. P. Jr. , Growth of analytic functions along a line, J. Anal. Math., 4 (1954), 1–28.Google Scholar
4. de Branges, L., Local operators on Fourier transforms, Duke Math. J., 25 (1958), 143–154.Google Scholar
5. de Branges, L., The a-local operator problem, Can. J. Math., 11 (1959), 583–592.Google Scholar
6. de Branges, L., The Stone-Weierstrass theorem, Proc. Amer. Math. Soc, 10 (1959), 822–824.Google Scholar
7. de Branges, L., The Bernstein problem, Proc. Amer. Math. Soc, 10 (1959), 825–832.Google Scholar
7. de Branges, L., Some mean squares of entire functions, Proc Amer. Math. Soc, 10 (1959), 833–839.Google Scholar
9. de Branges, L., Some Hilbert spaces of entire functions, Proc. Amer. Math. Soc, 10 (1959), 840–846.Google Scholar
10. de Branges, L., Some Hilbert spaces of entire functions, Trans. Amer. Math. Soc, 96 (1960), 259– 295.Google Scholar
11. de Branges, L., \\% Some Hilbert spaces of entire functions II, Trans. Amer. Math. Soc, 99 (1961), 118–152.Google Scholar
12. de Branges, L., Some Hilbert spaces of entire functions III, Trans. Amer. Math. Soc, 100 (1961), 73–115.Google Scholar
13. de Branges, L., Some Hilbert spaces of entire functions, IV, Trans. Amer. Math. Soc, 105 (1962), 43–83.Google Scholar
14. de Branges, L., Homogeneous and periodic spaces of entire functions, Duke Math. J., 29 (1962), 203–224.Google Scholar
15. de Branges, L., Symmetry in spaces of entire functions, Duke Math. J., 29 (1962), 383–392.Google Scholar
16. de Branges, L., Entire functions and integral transforms, Bull. Amer. Math. Soc, 67 (1961), 103– 106.Google Scholar
17. Levinson, N., Gap and density theorems, Amer. Math. Soc. Colloquium Publications, 26 (1940).Google Scholar