Overview

This book contains lectures presented at the MIT symposium on the 100th anniversary of Norbert Wiener's birth held in October 1994. The topics reflect Wiener's main interests while emphasizing current developments. In addition to lectures dealing directly with problems on which Wiener worked, such as potential theory, harmonic analysis, Wiener-Hopf theory, and Paley-Wiener theory, the book discusses the following topics: * Fourier integral operators with complex phase (a contemporary successor to the Paley-Wiener theory) * statistical aspects of quantum mechanics and of liquid crystals * financial markets, including the new trading strategies for options based on Wiener processes * statistical methods of genetic research * models of the nervous system, pattern recognition, and the nature of intelligence The volume includes reviews on Norbert Wiener's contributions from historical and current perspectives. This book gives mathematical researchers an overview of new mathematical problems presented by other areas and gives researchers in other fields a broad overview of the ways in which advanced mathematics might be useful to them. This text will also be of interest to those working in applications.

Full Product Details

Author:   American Mathematical Society ,  I. M. Singer ,  Daniel W. Stroock
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   No. 60
Weight:   0.964kg
ISBN:  

9780821804155

ISBN 10:   0821804154
Pages:   405
Publication Date:   30 June 1997
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Temporarily unavailable  
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Table of Contents

Biographical and Historical Remarks: Norbert Weiner by D. Jerison and D. W. Stroock The rise and fall of cybernetics in the US and the USSR by P. Elias Reminiscences of Norbert Wiener by D. Struik Speech by Fagi Levinson Some memories of Norbert Wiener by P. A. Samuelson Scientific Articles: Gibbs measures, quasi-periodic solutions and nonlinear partial differential equations by J. Bourgain Wiener's Tauberian theorem by L. Carleson The role of Paley-Wiener theory in partial differential equations by L. Ehrenpreis Paley-Wiener on manifolds by V. Guillemin Norbert Wiener and the development of mathematical engineering by T. Kailath Oscillating networks of neurons: Mathematics and function by N. Kopell Mapping heredity: Using probabilistic models and algorithms to map genes and genomes by E. S. Lander A non-random walk down Wall Street by A. W. Lo Filtered Wiener space versus abstract Wiener space by P. Malliavin Unsolved problems connected with the Wiener criterion by V. Mazya On the role of the Wiener process in finance theory and practice: The case of replicating portfolios by R. C. Merton Inference, learning, and recognition by S. K. Mitter Issues in the mathematical modeling of cortical functioning and thought by D. Mumford Polymer braids and iterated Moire maps by D. R. Nelson and R. D. Kamien Networks that learn and how the brain works by T. Poggio The risk management revolution by C. S. Sanford, Jr. and D. Borge Complex noncommutative infinite dimensional analysis and Fermion-Boson interactions by I. Segal Complex integral transforms, diffraction, resonances and phase space tunneling by J. Sjostrand Scaling, the free field and statistical mechanics by T. Spencer Weiner-Hopf integral equations by H. Widom.

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