Actions of holomorphic maps on spaces of holomorphic functions
Seiten
1995
Scuola Normale Superiore (Verlag)
978-88-7642-275-1 (ISBN)
Scuola Normale Superiore (Verlag)
978-88-7642-275-1 (ISBN)
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Investigates some aspects of the geometry and function theory on domains in complex vector spaces. This book focuses on bounded symmetric domains. It describes the theory of Riemann surfaces.
This thesis is devoted to investigating some aspects of the geometry and function theory on domains in complex vector spaces. The link between geometry and function theory stems from the standard approach whereby, if D is a domain in Cn, S is a semigroup of holomorphic maps of D into itself, and Hol(D) is the space of all scalar valued holomorphic functions on D, then S induces a semigroup of linear operators on Hol(D) whose invariant subspaces give information on the structure of S. In the one-dimensional case, the theory of Riemann surfaces leads to precise results. Passing from one to several complex variables the situation changes radically. In order to obtain further information on Aut D, one has to drastically restrict the class of bounded domains D under consideration, focusing the attention on bounded homogeneous domains or even on the narrower class of bounded symmetric domains.
This thesis is devoted to investigating some aspects of the geometry and function theory on domains in complex vector spaces. The link between geometry and function theory stems from the standard approach whereby, if D is a domain in Cn, S is a semigroup of holomorphic maps of D into itself, and Hol(D) is the space of all scalar valued holomorphic functions on D, then S induces a semigroup of linear operators on Hol(D) whose invariant subspaces give information on the structure of S. In the one-dimensional case, the theory of Riemann surfaces leads to precise results. Passing from one to several complex variables the situation changes radically. In order to obtain further information on Aut D, one has to drastically restrict the class of bounded domains D under consideration, focusing the attention on bounded homogeneous domains or even on the narrower class of bounded symmetric domains.
| Erscheint lt. Verlag | 1.10.1995 |
|---|---|
| Reihe/Serie | Publications of the Scuola Normale Superiore |
| Zusatzinfo | XIII, 159 p. |
| Verlagsort | Pisa |
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 88-7642-275-7 / 8876422757 |
| ISBN-13 | 978-88-7642-275-1 / 9788876422751 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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