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Complex Analysis
eBook - A Functional Analytic Approach, de Gruyter Textbook
ISBN/EAN: 9783110426151
Umbreit-Nr.: 8484870
Sprache:
Englisch
Umfang: 347 S.
Format in cm:
Einband:
Keine Angabe
Erschienen am 20.11.2017
Auflage: 1/2017
E-Book
Format: EPUB
DRM: Adobe DRM
- Zusatztext
- <p>In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchys integral theorem general versions of Runges approximation theorem and Mittag-Lefflers 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.</p><p><strong>Contents</strong><br>Complex numbers and functions<br>Cauchys Theorem and Cauchys formula<br>Analytic continuation<br>Construction and approximation of holomorphic functions<br>Harmonic functions<br>Several complex variables<br>Bergman spaces<br>The canonical solution operator to<br>Nuclear Fréchet spaces of holomorphic functions<br>The -complex<br>The twisted -complex and Schrödinger operators</p>
- Kurztext
- 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: Frechet 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 Frechet spaces of holomorphic functionsThe -complexThe twisted -complex and Schrodinger operators
- Autorenportrait
- <p><strong>Friedrich Haslinger</strong>, University of Vienna, Austria.</p>