| Edition |
1st ed. |
| Description |
1 online resource (xii, 365 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
North-Holland mathematics studies ; 187 |
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North-Holland mathematics studies ; 187.
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| Summary |
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 feature is that the approach adopted has allowed the extension of this theory to locally convex spaces, thereby including certain differential operators, which appear naturally in distribution spaces. The bulk of the second part of the book is dedicated to powers with pure imaginary exponents, which have been the focus of research in recent years, ever since the publication in 1987 of the now classic paper by G. Dore and A. Venni. Special care has been taken to give versions of the results with more accurate hypotheses, particularly with respect to the density of the domain or the range of the operator. The authors have made a point of making the text clear and self-contained. Accordingly, an extensive appendix contains the material on real and functional analysis used and, at the end of each chapter there are detailed historical and bibliographical notes in order to understand the development and current state of research into the questions dealt with. |
| Bibliography |
Includes bibliographical references (pages 347-360) and index. |
| Note |
Print version record. |
| Contents |
Non-negative operators -- Differential operators -- Balakrishnan operator -- Extension of the hirsch functional calculus -- Fractional powers of operators -- Domains, uniqueness and the cauchy problem -- Negative and imaginary powers -- Dore-venni theorem -- Functional calculus for C0-groups -- Imaginary powers on hilbert spaces -- Fractional powers and interpolation spaces -- Fractional powers of some differential operators. |
| Access |
Use copy Restrictions unspecified star MiAaHDL |
| Reproduction |
Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2010. MiAaHDL |
| System Details |
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
| Processing Action |
digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL |
| Subject |
Fractional powers.
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Puissances fractionnaires.
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MATHEMATICS -- Functional Analysis.
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Fractional powers
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Operatortheorie
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| Added Author |
Sanz Alix, Miguel.
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| Other Form: |
Print version: Martínez Carracedo, Celso. Theory of fractional powers of operators. 1st ed. Amsterdam ; New York : Elsevier, 2001 0444887970 9780444887979 (DLC) 2001268814 (OCoLC)45991107 |
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Online version: Martínez Carracedo, Celso. Theory of fractional powers of operators. 1st ed. Amsterdam ; New York : Elsevier, 2001 (OCoLC)760315639 |
| ISBN |
9780444887979 |
|
0444887970 |
|
0585474516 (electronic bk.) |
|
9780585474519 (electronic bk.) |
| Standard No. |
AU@ 000048130096 |
|
AU@ 000062579079 |
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CHNEW 001005784 |
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DEBBG BV036962257 |
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DEBBG BV039830125 |
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DEBBG BV042317271 |
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DEBSZ 276791622 |
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DEBSZ 482352515 |
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NZ1 12434596 |
|
