Regularised Integrals, Sums and Traces: An Analytic Point of View (University Lecture Series, 59, Band 59) - Softcover

Paycha, Sylvie

9780821853672: Regularised Integrals, Sums and Traces: An Analytic Point of View (University Lecture Series, 59, Band 59)

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ISBN 10: 0821853678 ISBN 13: 9780821853672

Verlag: American Mathematical Society, 2012

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Paycha seeks to clarify some aspects of regularization techniques, which are used to make sense of divergent integrals, discrete sums, or traces. There is nothing groundbreaking here, she says, just a unified perspective based on pedestrian proofs on results scattered in the physics and mathematics literature. Among her topics are the gamma function extended to non-positive integer points, the non-commutative residue as a complex residue, the canonical sum on non-integer order classical symbols, weighted traces, and anomalies of regularized determinants. Annotation �2013 Book News, Inc., Portland, OR (booknews.com)

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�ber die Autorin bzw. den Autor

Sylvie Paycha, Universit�t Potsdam, Potsdam, Germany and Universit� Blaise Pascal, Aubi�re, Cedex, France

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Verlag: American Mathematical Society
Erscheinungsdatum: 2012
Sprache: Englisch
ISBN 10: 0821853678
ISBN 13: 9780821853672
Einband: Taschenbuch
Anzahl der Seiten: 190
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Regularised Integrals, Sums and Traces

Sylvie Paycha

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Regularised Integrals, Sums and Traces : An Analytic Point of View

Paycha, Sylvie

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Regularised Integrals, Sums and Traces

Sylvie Paycha

Verlag: American Mathematical Society, US, 2013

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Paperback. Zustand: New. ``Regularization techniques'' is the common name for a variety of methods used to make sense of divergent series, divergent integrals, or traces of linear operators in infinite-dimensional spaces. Such methods are often indispensable in problems of number theory, geometry, quantum field theory, and other areas of mathematics and theoretical physics. However arbitrary and noncanonical they might seem at first glance, regularized sums, integrals, and traces often contain canonical concepts, and the main purpose of this book is to illustrate and explain this. This book provides a unified and self-contained mathematical treatment of various regularization techniques. The author shows how to derive regularized sums, integrals, and traces from certain canonical building blocks of the original divergent object. In the process of putting together these ``building blocks'', one encounters many problems and ambiguities caused by various so-called anomalies, which are investigated and explained in detail. Nevertheless, it turns out that the corresponding canonical sums, integrals, sums, and traces are well behaved, thus making the regularization procedure possible and manageable. This new unified outlook on regularization techniques in various fields of mathematics and in quantum field theory can serve as an introduction for anyone from a beginning mathematician interested in the subject to an experienced physicist who wants to gain a unified outlook on techniques he/she uses on a daily basis. Bestandsnummer des Verk�ufers LU-9780821853672

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Regularised Integrals, Sums and Traces: An Analytic Point of View (University Lecture Series)

Sylvie Paycha

Verlag: American Mathematical Society, 2012

ISBN 10: 0821853678 ISBN 13: 9780821853672

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Zustand: New. Provides a unified and self-contained mathematical treatment of various regularization techniques. The author shows how to derive regularized sums, integrals, and traces from certain canonical building blocks of the original divergent object. Series: University Lecture Series. Num Pages: 193 pages, Illustrations. BIC Classification: PBH. Category: (G) General (US: Trade). Dimension: 254 x 178. . . 2012. Paperback. . . . . Bestandsnummer des Verk�ufers V9780821853672

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