Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-26T08:53:56.068Z Has data issue: false hasContentIssue false
  • English
  • Français

Composition Operators

Published online by Cambridge University Press:  20 November 2018

Eric A. Nordgren
Eric A. Nordgren*
Affiliation:
University of New Hampshire, Durham, N.H.
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.

The object of this note is to report on some of the properties of a class of operators induced by inner functions. If m is normalized Lebesgue measure on the unit circle X in the complex plane and Cϕ is an inner function (a complex function on X of unit modulus almost everywhere whose Poisson integral is a non-constant holomorphic function in the open unit disk), then an operator Cϕ on L2(m) is defined by

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 442 - 449
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

Work supported in part by a grant from the National Science Foundation.

References

1. Brown, A., On a class of operators, Proc. Amer. Math. Soc, 4 (1953), 723–728.Google Scholar
2. Ford, L. R., Automorphic functions (New York, 1929).Google Scholar
3. Halmos, P. R., Shifts on Hilbert spaces, J. Reine Angew. Math., 208 (1961), 102–112.Google Scholar
4. Hoffman, K., Banach spaces of analytic functions (Englewood Cliffs, N.J., 1962).Google Scholar