Complex analysis: a functional analytic approach
In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy‘s integral theorem general versions of Runge‘s approximation theorem and Mittag-Leffler‘s theorem are discussed. The fi rst part ends with an analytic characterization...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2018]
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| Series: | De Gruyter Textbook
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| Subjects: | |
| Online Access: | DE-1043 DE-1046 DE-573 DE-898 DE-859 DE-860 DE-20 DE-706 DE-739 DE-858 Volltext |
| Summary: | In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy‘s integral theorem general versions of Runge‘s approximation theorem and Mittag-Leffler‘s theorem are discussed. The fi rst part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. ContentsComplex numbers and functionsCauchy’s Theorem and Cauchy’s formulaAnalytic continuationConstruction and approximation of holomorphic functionsHarmonic functionsSeveral complex variablesBergman spacesThe canonical solution operator to Nuclear Fréchet spaces of holomorphic functionsThe -complexThe twisted -complex and Schrödinger operators |
| Physical Description: | 1 Online-Ressource (X, 338 Seiten) 30 Illustrationen |
| ISBN: | 9783110417241 |
| DOI: | 10.1515/9783110417241 |
Staff View
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| 520 | |a In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy‘s integral theorem general versions of Runge‘s approximation theorem and Mittag-Leffler‘s theorem are discussed. The fi rst part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. ContentsComplex numbers and functionsCauchy’s Theorem and Cauchy’s formulaAnalytic continuationConstruction and approximation of holomorphic functionsHarmonic functionsSeveral complex variablesBergman spacesThe canonical solution operator to Nuclear Fréchet spaces of holomorphic functionsThe -complexThe twisted -complex and Schrödinger operators | ||
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| institution | BVB |
| isbn | 9783110417241 |
| language | English |
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| spelling | Haslinger, Friedrich Verfasser (DE-588)1053550928 aut Complex analysis a functional analytic approach Friedrich Haslinger Berlin ; Boston De Gruyter [2018] © 2018 1 Online-Ressource (X, 338 Seiten) 30 Illustrationen txt rdacontent c rdamedia cr rdacarrier De Gruyter Textbook In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy‘s integral theorem general versions of Runge‘s approximation theorem and Mittag-Leffler‘s theorem are discussed. The fi rst part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. ContentsComplex numbers and functionsCauchy’s Theorem and Cauchy’s formulaAnalytic continuationConstruction and approximation of holomorphic functionsHarmonic functionsSeveral complex variablesBergman spacesThe canonical solution operator to Nuclear Fréchet spaces of holomorphic functionsThe -complexThe twisted -complex and Schrödinger operators In English analytic continuation Bergman kernel Cauchy integral theorem Complex analysis Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 Erscheint auch als Druck-Ausgabe 978-3-11-041723-4 https://doi.org/10.1515/9783110417241 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Haslinger, Friedrich Complex analysis a functional analytic approach analytic continuation Bergman kernel Cauchy integral theorem Complex analysis Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4018935-1 |
| title | Complex analysis a functional analytic approach |
| title_auth | Complex analysis a functional analytic approach |
| title_exact_search | Complex analysis a functional analytic approach |
| title_full | Complex analysis a functional analytic approach Friedrich Haslinger |
| title_fullStr | Complex analysis a functional analytic approach Friedrich Haslinger |
| title_full_unstemmed | Complex analysis a functional analytic approach Friedrich Haslinger |
| title_short | Complex analysis |
| title_sort | complex analysis a functional analytic approach |
| title_sub | a functional analytic approach |
| topic | analytic continuation Bergman kernel Cauchy integral theorem Complex analysis Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | analytic continuation Bergman kernel Cauchy integral theorem Complex analysis Funktionentheorie |
| url | https://doi.org/10.1515/9783110417241 |
| work_keys_str_mv | AT haslingerfriedrich complexanalysisafunctionalanalyticapproach |