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 char...
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|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Berlin
De Gruyter
2018
Walter de Gruyter GmbH |
| Vydání: | 1 |
| Edice: | De Gruyter Textbook |
| Témata: | |
| ISBN: | 3110417235, 9783110417234 |
| On-line přístup: | Získat plný text |
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| Abstract | 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. |
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| AbstractList | 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 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. In this textbook an elegant and fresh approach to complex analysis of single and multiple variables is presented. After an introduction of Cauchy's integral theorem and analytic continuation, harmonic functions are discussed in the first part. The second part is concerned with functional analytic methods, such as the Bergman-Kernel, to tackle the theory of multiple variables. |
| Author | Haslinger, Friedrich |
| Author_xml | – sequence: 1 fullname: Haslinger, Friedrich |
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| Edition | 1 1st edition. |
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| Keywords | analytic continuation Cauchy integral theorem Complex analysis Bergman kernel |
| LCCallNum_Ident | QA39.3 .H375 2018 |
| Language | English |
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| Notes | Includes bibliographical references (p. [331]-333) and index |
| OCLC | 1013729242 |
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| Snippet | 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... 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... In this textbook an elegant and fresh approach to complex analysis of single and multiple variables is presented. After an introduction of Cauchy's integral... 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... |
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| SubjectTerms | analytic continuation Bergman kernel Cauchy integral theorem Complex analysis MATHEMATICS / Complex Analysis MATHEMATICS / Functional Analysis Mathematics-Textbooks |
| TableOfContents | Intro -- Preface -- Contents -- 1. Complex numbers and functions -- 2. Cauchy's Theorem and Cauchy's formula -- 3. Analytic continuation -- 4. Construction and approximation of holomorphic functions -- 5. Harmonic functions -- 6. Several complex variables -- 7. Bergman spaces -- 8. The canonical solution operator to ∂̄ -- 9. Nuclear Fréchet spaces of holomorphic functions -- 10. The ∂̄-complex -- 11. The twisted ∂̄-complex and Schrödinger operators -- Bibliography -- Index 2. Cauchy’s Theorem and Cauchy’s formula -- Contents -- 9. Nuclear Fréchet spaces of holomorphic functions -- Preface -- 5. Harmonic functions -- 1. Complex numbers and functions -- 7. Bergman spaces -- Index 6. Several complex variables -- 10. The ∂̄-complex -- 3. Analytic continuation -- Frontmatter -- 11. The twisted ∂̄-complex and Schrödinger operators -- 4. Construction and approximation of holomorphic functions -- Bibliography -- 8. The canonical solution operator to ∂̄ -- |
| Title | Complex analysis : a functional analytic approach |
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