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Bernstein Functions: Theory and Applications (De Gruyter Studies in Mathematics, 37) - Hardcover

 
9783110252293: Bernstein Functions: Theory and Applications (De Gruyter Studies in Mathematics, 37)
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Bernstein functions and the important subclass of complete Bernstein functions appear in various fields of mathematics - often with different definitions and under different names. Probabilists, for example, know Bernstein functions as Laplace exponents, and in harmonic analysis they are called negative definite functions. Complete Bernstein functions are used in complex analysis under the name Pick or Nevanlinna functions, while in matrix analysis and operator theory, the name operator monotone function is more common. When studying the positivity of solutions of Volterra integral equations, various types of kernels appear which are related to Bernstein functions. There exists a considerable amount of literature on each of these classes, but only a handful of texts observe the connections between them or use methods from several mathematical disciplines. This monograph - now in its second revised and extended edition - is about these connections. Compared to the first edition the authors added a substantial amount of new material. Their aim was to retain the overall structure of the text with theoretical material in Chapters 1 to 11 and more specific applications in Chapters 12 to 15.

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About the Author:
Rene L. Schilling, Dresden University of Technology, Germany; Renming Song, University of Illinois, Urbana, USA; Zoran Vondracek, University of Zagreb, Croatia.
Review:

"To sum up, the book collects and integrates results from a number of sources scattered throughout the literature. It is clearly and carefully written. It will certainly be useful for both graduate students and researchers in different areas." Mathematical Reviews (review of the first edition)

"This impressive monograph, which is now in an expanded second edition, does a wonderful job of collecting together and synthesising some of the most important results and applications. Consequently it represents a unique perspective on this important function class which will be a valuable resource for many years to come for both experienced researchers and graduate students." Mathematical Reviews

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  • PublisherDe Gruyter
  • Publication date2012
  • ISBN 10 3110252295
  • ISBN 13 9783110252293
  • BindingHardcover
  • Edition number2
  • Number of pages424

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9783110215304: Bernstein Functions: Theory and Applications (De Gruyter Studies in Mathematics, 37)

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ISBN 10:  ISBN 13:  9783110215304
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  • 9783110269000: Bernstein Functions: Theory and Applications (de Gruyter Studies in Mathematics)

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Book Description Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Bernstein functions appear in various fields of mathematics, e.g. probability theory, potential theory, operator theory, functional analysis and complex analysis often with different definitions and under different names. Among the synonyms are `Laplace exponent' instead of Bernstein function, and complete Bernstein functions are sometimes called `Pick functions', `Nevanlinna functions' or `operator monotone functions'. This monograph now in its second revised and extended edition offers a self-contained and unified approach to Bernstein functions and closely related function classes, bringing together old and establishing new connections. For the second edition the authors added a substantial amount of new material. As in the first edition Chapters 1 to 11 contain general material which should be accessible to non-specialists, while the later Chapters 12 to 15 are devoted to more specialized topics. An extensive list of complete Bernstein functions with their representations is provided. 424 pp. Englisch. Seller Inventory # 9783110252293

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Book Description Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. To sum up, the book collects and integrates results from a number of sources scattered throughout the literature. It is clearly and carefully written. It will certainly be useful for both graduate students and researchers in different areas. Mathem. Seller Inventory # 4455990

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Book Description Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Bernstein functions appear in various fields of mathematics, e.g. probability theory, potential theory, operator theory, functional analysis and complex analysis often with different definitions and under different names. Among the synonyms are `Laplace exponent' instead of Bernstein function, and complete Bernstein functions are sometimes called `Pick functions', `Nevanlinna functions' or `operator monotone functions'. This monograph now in its second revised and extended edition offers a self-contained and unified approach to Bernstein functions and closely related function classes, bringing together old and establishing new connections. For the second edition the authors added a substantial amount of new material. As in the first edition Chapters 1 to 11 contain general material which should be accessible to non-specialists, while the later Chapters 12 to 15 are devoted to more specialized topics. An extensive list of complete Bernstein functions with their representations is provided. Seller Inventory # 9783110252293

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