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Bernstein Functions

Theory and Applications

René L. Schilling, Renming Song, Zoran Vondracek (Autoren)

Buch | Hardcover

XIV, 410 Seiten

2012 | 2nd rev. and ext. ed.
De Gruyter (Verlag)
978-3-11-025229-3 (ISBN)

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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

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.

René L. Schilling, Dresden University of Technology, Germany; Renming Song, University of Illinois, Urbana, USA; Zoran Vondraček, University of Zagreb, Croatia.

"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

Erscheint lt. Verlag	14.9.2012
Reihe/Serie	De Gruyter Studies in Mathematics ; 37
Zusatzinfo	5 b/w ill., 10 b/w tbl.
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	170 x 240 mm
Gewicht	836 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Bernstein Function • Bernstein Function; Monotone Function; Probability Measure; Semigroup; Theory • Bernstein Funktion • Bernstein-Funktion • Mathematik • Monotone Function • Monotone Funktion • probability measure • Semigroup • theory
ISBN-10	3-11-025229-5 / 3110252295
ISBN-13	978-3-11-025229-3 / 9783110252293
Zustand	Neuware