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Complex Analysis : A Functional Analytic Approach

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Title: Complex Analysis : A Functional Analytic Approach
Description: 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
Authors: Friedrich Haslinger
Resource Type: eBook.
Subjects: Mathematics--Textbooks
Categories: MATHEMATICS / Complex Analysis, MATHEMATICS / Functional Analysis
Database: eBook Collection (EBSCOhost)
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An: 1639770
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  Label: Title
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  Data: Complex Analysis : A Functional Analytic Approach
– Name: Abstract
  Label: Description
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  Data: 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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  Data: <searchLink fieldCode="AR" term="%22Friedrich+Haslinger%22">Friedrich Haslinger</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Mathematics--Textbooks%22">Mathematics--Textbooks</searchLink>
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  Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Complex+Analysis%22">MATHEMATICS / Complex Analysis</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Functional+Analysis%22">MATHEMATICS / Functional Analysis</searchLink>
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RecordInfo BibRecord:
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    Classifications:
      – Code: 510
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Mathematics--Textbooks
        Type: general
    Titles:
      – TitleFull: Complex Analysis : A Functional Analytic Approach
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Friedrich Haslinger
      – PersonEntity:
          Name:
            NameFull: Friedrich Haslinger
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2018
            – D: 12
              M: 04
              Type: profile
              Y: 2018
          Identifiers:
            – Type: isbn-print
              Value: 9783110417234
            – Type: isbn-electronic
              Value: 9783110417241
            – Type: isbn-electronic
              Value: 9783110426151
          Titles:
            – TitleFull: Complex Analysis : A Functional Analytic Approach
              Type: main
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