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Mathematics and Its Applications

White Noise

An Infinite Dimensional Calculus

Authors: Hida, T., Hui-Hsiung Kuo, Potthoff, J., Streit, W.

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  • ISBN 978-94-017-3680-0
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Hardcover $159.99
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About this book

Many areas of applied mathematics call for an efficient calculus in infinite dimensions. This is most apparent in quantum physics and in all disciplines of science which describe natural phenomena by equations involving stochasticity. With this monograph we intend to provide a framework for analysis in infinite dimensions which is flexible enough to be applicable in many areas, and which on the other hand is intuitive and efficient. Whether or not we achieved our aim must be left to the judgment of the reader. This book treats the theory and applications of analysis and functional analysis in infinite dimensions based on white noise. By white noise we mean the generalized Gaussian process which is (informally) given by the time derivative of the Wiener process, i.e., by the velocity of Brownian mdtion. Therefore, in essence we present analysis on a Gaussian space, and applications to various areas of sClence. Calculus, analysis, and functional analysis in infinite dimensions (or dimension-free formulations of these parts of classical mathematics) have a long history. Early examples can be found in the works of Dirichlet, Euler, Hamilton, Lagrange, and Riemann on variational problems. At the beginning of this century, Frechet, Gateaux and Volterra made essential contributions to the calculus of functions over infinite dimensional spaces. The important and inspiring work of Wiener and Levy followed during the first half of this century. Moreover, the articles and books of Wiener and Levy had a view towards probability theory.

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $119.00
price for USA in USD
  • ISBN 978-94-017-3680-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase Institutional customers should get in touch with their account manager
Hardcover $159.99
price for USA in USD
Softcover $159.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
White Noise
Book Subtitle
An Infinite Dimensional Calculus
Authors
Series Title
Mathematics and Its Applications
Series Volume
253
Copyright
1993
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-017-3680-0
DOI
10.1007/978-94-017-3680-0
Hardcover ISBN
978-0-7923-2233-7
Softcover ISBN
978-90-481-4260-6
Edition Number
1
Number of Pages
XIV, 520
Topics