UID:
almahu_9947368001802882
Format:
1 online resource (379 p.)
Edition:
1st ed.
ISBN:
1-281-05859-9
,
9786611058593
,
0-08-051907-5
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0-585-47451-6
Series Statement:
North-Holland mathematics studies ; 187
Content:
This book makes available to researchers and advanced graduates a simple and direct presentation of the fundamental aspects of the theory of fractional powers of non-negative operators, which have important links with partial differential equations and harmonic analysis. For the first time ever, a book deals with this subject monographically, despite the large number of papers written on it during the second half of the century. The first chapters are concerned with the construction of a basic theory of fractional powers and study the classic questions in that respect. A new and distinct featu
Note:
Description based upon print version of record.
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Front Cover; The Theory of Fractional Powers of Operators; Copyright Page; Contents; Introduction; Chapter 1. Non-Negative Operators; 1.1 Definition and Basic Properties; 1.2 Sectorial Operators; 1.3 Examples of Non-Negative Operators; 1.4 Non-Negative Operators in Locally Convex Spaces; 1.5 Notes on Chapter 1; Chapter 2. Differential Operators; 2.1 Operators of Riemann-Liouville and Weyl; 2.2 The Derivative Operator in R; 2.3 The Laplacian Operator; 2.4 Second-Order Elliptic Differential Operators; 2.5 The Laplacian in a Locally Convex Space of Distributions; 2.6 Notes on Chapter 2
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Chapter 3. The Balakrishnan Operator3.1 Definition of Balakrishnan and Basic Properties; 3.2 Expressions of the Balakrishnan Operator when - A is the Infinitesimal Generator of an Equibounded Co-Semigroup; 3.3 Examples; 3.4 Notes on Chapter 3; Chapter 4. An Extension of the Hirsch Functional Calculus; 4.1 Classes of Functions Associated to Radon Measures; 4.2 Functional Calculus; 4.3 Spectral Mapping Theorem; 4.4 Hirsch Functional Calculus in Locally Convex Spaces; 4.5 Notes on Chapter 4; Chapter 5. Fractional Powers of Operators; 5.1 Definition of Fractional Power . Additivity
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5.2 Representations of the Fractional Powers5.3 Spectral Mapping Theorem; 5.4 Sectoriality of the Fractional Powers . Multiplicativity; 5.5 Semigroups Generated by Fractional Powers; 5.6 Fractional Powers of Operators in Locally Convex Spaces; 5.7 Notes on Chapter 5; Chapter 6. Domains, Uniqueness and the Cauchy Problem; 6.1 Domains of Fractional Powers; 6.2 Conditions for Uniqueness; 6.3 The Second - Order Abstract Incomplete Cauchy Problem; 6.4 Results in Locally Convex Spaces; 6.5 Notes on Chapter 6; Chapter 7. Negative and Imaginary Powers; 7.1 Definitions and Basic Properties
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7.2 The Balakrishnan and Komatsu Operators7.3 Examples; 7.4 Limit Operators Related to the Imaginary Power; 7.5 Negative and Imaginary Powers on Locally Convex Spaces; 7.6 Notes on Chapter 7; Chapter 8. The Dore-Venni Theorem; 8.1 Definitions and Notations; 8.2 Sectoriality and Boundedness of Exponential Type; 8.3 The Dore Venni Theorem; 8.4 Sum of Closed Operators in UMD Spaces; 8.5 LP Maximal Regularity; 8.6 Notes on Chapter 8; Chapter 9. Functional Calculus for Co-groups; 9.1 The Mellin Transform; 9.2 Functional Calculus for Co-groups
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9.3 Analytic Generators . Imaginary Powers of the Product9.4 Imaginary Powers of the Sum of Operators; 9.5 Notes on Chapter 9; Chapter 10. Imaginary Powers on Hilbert Spaces; 10.1 Logarithms; 10.2 Bounded Functional Calculus; 10.3 Notes on Chapter 10; Chapter 11. Fractional Powers and Interpolation Spaces; 11.1 Introduction; 11.2 Interpolation Spaces . The Real Method; 11.3 Komatsu's Spaces; 11.4 Komatsu's Spaces and Real Interpolation Spaces; 11.5 Domains of Fractional Powers and the Komatsu Spaces; 11.6 Interpolation Spaces . The Complex Method; 11.7 Notes on Chapter 11
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Chapter 12. Fractional Powers of some Differential Operators
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English
Additional Edition:
ISBN 0-444-88797-0
Language:
English
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