Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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

Mathematics --- Bergman kernel. --- Cauchy integral theorem. --- Complex analysis. --- analytic continuation.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Faisceaux, Théorie des. --- Prolongement analytique. --- WKB, Approximation. --- Sheaf theory. --- Analytic continuation. --- WKB approximation.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Infinite dimensional holomorphy and applications

Holomorphic functions --- Domains of holomorphy --- Holomorphy domains --- Analytic continuation --- Functions of several complex variables --- Functions, Holomorphic

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Functional Analysis, Holomorphy and Approximation Theory

Functional analysis --- Holomorphic functions --- Domains of holomorphy --- Approximation theory --- Holomorphy domains --- Analytic continuation --- Functions of several complex variables --- Functions, Holomorphic

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents a set of basic properties of holomorphic mappings between complex normed spaces and between complex locally convex spaces. These properties have already achieved an almost definitive form and should be known to all those interested in the study of infinite dimensional Holomorphy and its applications.The author also makes ``incursions'' into the study of the topological properties of the spaces of holomorphic mappings between spaces of infinite dimension. An attempt is then made to show some of the several topologies that can naturally be considered in these spaces.