UID:
almahu_9947367604502882
Umfang:
1 online resource (106 p.)
ISBN:
1-281-77333-6
,
9786611773335
,
0-08-087115-1
Serie:
North-Holland mathematics studies ; 4
Inhalt:
Spectral theory and complex analysis
Anmerkung:
Description based upon print version of record.
,
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
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3.1. Spectrum of elements in a Banach algebra3.2. 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)
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5.3. Decomposition property for subalgebras5.4. 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
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BlBLIOGRAPHY
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English
Weitere Ausg.:
ISBN 0-444-10429-1
Sprache:
Englisch
