# An introduction to complex analysis in several variables

@inproceedings{Hrmander1973AnIT, title={An introduction to complex analysis in several variables}, author={Lars H{\"o}rmander}, year={1973} }

I. Analytic Functions of One Complex Variable. II. Elementary Properties of Functions of Several Complex Variables. III. Applications to Commutative Banach Algebras. IV. L2 Estimates and Existence Theorems for the Operator. V. Stein Manifolds. VI. Local Properties of Analytic Functions. VII. Coherent Analytic Sheaves on Stein Manifolds. Bibliography. Index.

No Paper Link Available

## 2,135 Citations

Functions of Several Complex Variables

- Mathematics
- 2001

In this chapter, we shall define holomorphic functions of several complex variables. The essentially local theory given in Chapter 1, §§3, 4 extends to these functions with little effort. We shall…

UNIVERSAL HOLOMORPHIC FUNCTIONS IN SEVERAL VARIABLES

- Philosophy
- 1997

We consider universal holomorphic functions in several variables. Entire functions satisfying that their compositions with translations Me dense are called universal. Using the original constructive…

An Introduction to Analysis on Complex Manifolds

- Mathematics
- 1982

We give an account of some of the analysis on complex manifolds leading in particular to Dolbeault cohomology and the Hodge decomposition Theorem. On the way we introduce some basic notions such as…

Special functions and relations within complex clifford analysis I

- Mathematics
- 1983

We introduce a generalized Cauchy integral formula for special classes of functions, holomorphic in several complex variables. These functions also satisfy a generalized Cachy-Riemann equation. The…

Spectral Decompositions in Spaces of Analytic Functionals

- Mathematics
- 1980

This article deals with spaces of entire vector-valued functions determined by families of radial majorants, and their dual spaces of analytic functionals. Spectral properties of generalized boundary…

Harmonic Analysis Techniques in Several Complex Variables

- Mathematics
- 2014

We give a survey of recent joint work with E. M. Stein (Princeton University) concerning the application of suitable versions of the T(1)-theorem technique to the study of orthogonal projections onto…

Notes on algebras and vector spaces of functions

- Mathematics
- 2010

These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so…

The principal axis theorem for holomorphic functions

- Mathematics
- 1999

An algebraic approach to Rellich’s theorem is given which states that any analytic family of matrices which is normal on the real axis can be diagonalized by an analytic family of matrices which is…