A fixed point formula in one complex variable
We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernal of this domain. The Lefschetz number is proved to be the sum of usual con...
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Universität Potsdam
2003
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| Online Access: | http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26495 http://opus.kobv.de/ubp/volltexte/2008/2649/ |
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ndltd-Potsdam-oai-kobv.de-opus-ubp-26492013-01-08T00:55:06Z A fixed point formula in one complex variable Tarkhanov, Nikolai Mathematics We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernal of this domain. The Lefschetz number is proved to be the sum of usual contributions of fixed points of the map in D and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points. Universität Potsdam Mathematisch-Naturwissenschaftliche Fakultät. Institut für Mathematik 2003 Preprint application/pdf urn:nbn:de:kobv:517-opus-26495 http://opus.kobv.de/ubp/volltexte/2008/2649/ eng http://opus.kobv.de/ubp/doku/urheberrecht.php |
| collection |
NDLTD |
| language |
English |
| format |
Others
|
| sources |
NDLTD |
| topic |
Mathematics |
| spellingShingle |
Mathematics Tarkhanov, Nikolai A fixed point formula in one complex variable |
| description |
We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernal of this domain. The Lefschetz number is proved to be the sum of usual contributions of fixed points of the map in D and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points. |
| author |
Tarkhanov, Nikolai |
| author_facet |
Tarkhanov, Nikolai |
| author_sort |
Tarkhanov, Nikolai |
| title |
A fixed point formula in one complex variable |
| title_short |
A fixed point formula in one complex variable |
| title_full |
A fixed point formula in one complex variable |
| title_fullStr |
A fixed point formula in one complex variable |
| title_full_unstemmed |
A fixed point formula in one complex variable |
| title_sort |
fixed point formula in one complex variable |
| publisher |
Universität Potsdam |
| publishDate |
2003 |
| url |
http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26495 http://opus.kobv.de/ubp/volltexte/2008/2649/ |
| work_keys_str_mv |
AT tarkhanovnikolai afixedpointformulainonecomplexvariable AT tarkhanovnikolai fixedpointformulainonecomplexvariable |
| _version_ |
1716501719171465216 |