02915nam 2200493 450 991053623020332120230814221558.03-11-042615-310.1515/9783110417241(CKB)4100000001044512(MiAaPQ)EBC5158933(DE-B1597)450203(OCoLC)1013729242(DE-B1597)9783110417241(Au-PeEL)EBL5158933(CaPaEBR)ebr11473980(EXLCZ)99410000000104451220171222h20182018 uy 0engurcnu||||||||rdacontentrdamediardacarrierComplex analysis a functional analytic approach /Friedrich HaslingerBerlin, [Germany] ;Boston, [Massachusetts] :De Gruyter,2018.©20181 online resource (348 pages) illustrationsDe Gruyter Textbook3-11-041723-5 3-11-041724-3 Includes bibliographical references and index.Frontmatter -- 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 -- IndexIn 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 MathematicsTextbooksMathematics510Haslinger Friedrich1141604MiAaPQMiAaPQMiAaPQBOOK9910536230203321Complex analysis2680057UNINA