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Sur les Fonctions Analytiques Multiformes dont les Valeurs Sont des Segments

Published online by Cambridge University Press:  20 November 2018

Une Baribeau
Une Baribeau*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, 16, Mill Lane, Cambridge CB2 1SB, U.K.
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Abstract

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Analytic multivalued functions are a powerful tool in spectral theory. In this paper we study analytic multivalued functions λ → K(λ) whose values are segments. Under the additional assumption that K is continuous, we prove that the endpoints of K vary locally holomorphically.

Keywords

47A1032F15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990 , pp. 100 - 105
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Aupetit, B., Propriétés spectrales des algèbres de Banach, Lecture notes in Mathematics 735, Springer-Verlag, Heidelberg, 1979.Google Scholar
2. Aupetit, B., Analytic multivalued functions in Banach algebras and uniform algebras, Adv. Math 44 (1982), 18–60.Google Scholar
3. Aupetit, B., A Primer on Spectral Theory, livre à paraître.Google Scholar
4. Aupetit, B. et Baribeau, L., Sous-harmonicité de l'angle spectral, C.R. Math. Rep. Acad. Sci. Canada, 10 (1988), 51–56.Google Scholar
5. Oka, K., Note sur les familles de fonctions analytiques multiformes etc., J. Sci. Hiroshima Univ. Ser. A 4 (1934), 93–98.Google Scholar
6. Ransford, T. J., Analytic Multivalued Functions, Doctoral Thesis, University of Cambridge, 1983.Google Scholar
7. Słodkowski, Z., Analytic Set-Valued Functions and Spectra, Math. Ann. 256 (1981) 363–386.Google Scholar
8. Vesentini, E., Maximum theorems for spectra, dans Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham), pp 111-117, Springer-Verlag, New-York, 1970.Google Scholar