複素解析（テキスト） Complex Analysis : A Functional Analytic Approach (De Gruyter Textbook) （2017. IX, 338 S. 30 b/w ill. 240 mm）

Haslinger, Friedrich

DE GRUYTER（2017発売）

DE GRUYTER（2017発売）

• 製本 Paperback:紙装版/ペーパーバック版
• 商品コード 9783110417234

Full 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.

Contents
Complex numbers and functions
Cauchy's Theorem and Cauchy's formula
Analytic continuation
Construction and approximation of holomorphic functions
Harmonic functions
Several complex variables
Bergman spaces
The canonical solution operator to
Nuclear Fréchet spaces of holomorphic functions
The -complex
The twisted -complex and Schrödinger operators