Spectral Theory and Complex Analysis
Elsevier (Publisher)
Published on 26. August 2011
92 pages
978-0-08-087115-8 (ISBN)
Description
Spectral Theory and Complex Analysis
More details
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Content
- Front Cover
- Spectral Theory and Complex Analysis
- Copyright Page
- Contents
- INTRODUCTION
- LIST OF SYMBOLS
- CHAPTER I. ALGEBRAS OF HOLOMORPHIC FUNCTIONS WITH RESTRICTED GROWTH
- 1.1. Basic definitions
- 1.2. Weight functions
- 1.3. Elementary properties
- 1.4. Regularization of weight functions
- 1.5. Inductive limits
- Notes
- CHAPTER II. BOUNDEDNESS AND POLYNORMED VECTOR SPACES
- 2.1. Polynormed vector spaces
- 2.2. Convex bounded structures
- 2.3. Completeness
- 2.4. Closure and density
- 2.5. Algebras and ideals
- Notes
- CHAPTER III. SPECTRAL THEORY of b-ALGEBRAS
- 3.1. Spectrum of elements in a Banach algebra
- 3.2. Spectral sets
- 3.3. Spectral functions
- 3.4. The holomorphic functional calculus
- 3.5. Spectral theory modulo a b-ideal
- Notes
- CHAPTER IV. SPECTRAL THEOREMS AND HOLOMORPHIC CONVEXITY
- 4.1. Preliminaries
- 4.2. Spectral sets for z in O(d)
- 4.3. Spectral functions for z in O(d)
- 4.4. Plurisubharmonic regularization
- 4.5. Domains of holomorphy
- 4.6. Bounded multiplicative linear forms
- Notes
- CHAPTER V. DECOMPOSITION PROPERTY FOR ALGEBRAS OF HOLOMORPHIC FUNCTIONS
- 5.1. Preliminaries
- 5.2. Decomposition property for O(d)
- 5.3. Decomposition property for subalgebras
- 5.4. Spectral functions for z
- 5.5. Convexity with respect to algebras of holomorphic functions
- 5.6. Ideals of holomorphic functions
- Notes
- CHAPTER VI. APPROXIMATION THEOREMS
- 6.1. Approximation on compact sets
- 6.2. Runge domains and generalizations
- 6.3. Basic approximation theorem
- 6.4. Approximation with growth
- Notes
- CHAPTER VII. FILTRATIONS
- 7.1. Filtrated b - algebras
- 7.2. Spectral theorem with filtration
- 7.3. Application to plurisubharmonic functions
- 7.4. Approximation theorems with filtration
- 7.5. Polynomially convex open sets
- Notes
- BlBLIOGRAPHY
