White Noise

An Infinite Dimensional Calculus

  • Takeyuki Hida
  • Hui-Hsiung Kuo
  • Jürgen Potthoff
  • Ludwig Streit

Part of the Mathematics and Its Applications book series (MAIA, volume 253)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit
    Pages 1-9
  3. Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit
    Pages 10-34
  4. Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit
    Pages 35-73
  5. Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit
    Pages 74-145
  6. Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit
    Pages 146-183
  7. Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit
    Pages 184-231
  8. Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit
    Pages 232-276
  9. Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit
    Pages 277-316
  10. Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit
    Pages 317-365
  11. Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit
    Pages 366-398
  12. Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit
    Pages 399-434
  13. Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit
    Pages 435-450
  14. Back Matter
    Pages 451-516

About this book

Introduction

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.

Keywords

Brownian motion Dirichlet form Markov process Potential Probability theory measure theory

Authors and affiliations

  • Takeyuki Hida
    • 1
  • Hui-Hsiung Kuo
    • 2
  • Jürgen Potthoff
    • 3
  • Ludwig Streit
    • 4
    • 5
  1. 1.Department of MathematicsMeijo UniversityNagoyaJapan
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA
  3. 3.Universität MannheimMannheimGermany
  4. 4.BiBos, Universität BielefeldBielefeldGermany
  5. 5.Universidade da MadeiraFunchal, MadeiraPortugal

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-3680-0
  • Copyright Information Springer Science+Business Media B.V. 1993
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4260-6
  • Online ISBN 978-94-017-3680-0
  • About this book