Generalized Functions, Operator Theory, and Dynamical Systems: 1st Edition (Paperback) book cover

Generalized Functions, Operator Theory, and Dynamical Systems

1st Edition

By I Antoniou, G Lumer

Chapman and Hall/CRC

392 pages

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Paperback: 9780849306198
pub: 1998-12-23
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Nobel prize winner Ilya Prigogine writes in his preface: "Irreversibility is a challenge to mathematics…[which] leads to generalized functions and to an extension of spectral analysis beyond the conventional Hilbert space theory." Meeting this challenge required new mathematical formulations-obstacles met and largely overcome thanks primarily to the contributors to this volume."

This compilation of works grew out of material presented at the "Hyperfunctions, Operator Theory and Dynamical Systems" symposium at the International Solvay Institutes for Physics and Chemistry in 1997. The result is a coherently organized collective work that moves from general, widely applicable mathematical methods to ever more specialized physical applications. Presented in two sections, part one describes Generalized Functions and Operator Theory, part two addresses Operator Theory and Dynamical Systems.

The interplay between mathematics and physics is now more necessary than ever-and more difficult than ever, given the increasing complexity of theories and methods. Here the topics include:

Table of Contents

Part I: Generalized Functions and Operator Theory

An Introduction to Hyperfunctions and ?-expansions, G. Lumer

Partial Inner Product Spaces of Analytic Functions, J.-P. Antoine

Rigged Spectral States: A Proclivity for Eigenvalues, K. Gustafson

Densities of Singular Measures and Generalized Spectral Decompositions, I. Antoniou and Z. Suchanecki

Convolution Kernels and Generalized Functions, B. Bäumer, G. Lumer, and F. Neubrander

Spectral Theory of Closed Linear Operators on Banach Spaces from a Locally Convex Point of View, V. Wrobel

Ultradistributions and the Levinson Condition, I. Cioranescu and L. Zsido

Representation of the Derivatives and Products of the Delta Function in Hilbert Space, Yu. Melnikov

Series Representations of the Complex Delta Function, I. Antoniou, Z. Suchanecki, and S. Tasaki

Antieigenvalues: An Extended Spectral Theory, K. Gustafson

Part II: Operator Theory and Dynamical Systems

Laws of Nature, Probability, and Time Symmetry Breaking, I. Prigogine and T. Petrosky

Extended Spectral Decompositions of Evolution Operators, I. Antoniou and S. Shkarin

Some Little Things About Rigged Hilbert Spaces and Quantum Mechanics and All That, A. Bohm, M. Gadella, and S. Wickramasekara

Axiomatics of Thermodynamics and Quantum Chaos, V. Maslov

Stochastic Evolution on Product Manifolds. S. Albeverio, A. Daletskii, and Yu. Kondratiev

Interaction Problems with Distributions and Hyperfunctions Data, G. Lumer

Absolute Continuity of Convolutions of Singular Measures and New Branches of Spectrum of Liouvillians and Few-Body Hamiltonians, L Bos and B Pavlov

On Scattering Theories Involving Moving Boundaries, G. F. Roach

The Eigenvalue Problem for Networks of Beams, B Dekoninck and S Nicaise

Generalized Perturbations and Operator Relations, P Kurasov and B Pavlov

On Spectral Analysis of a Class of Integral-Difference Collision Operators, Yu. Melnikiv

Dynamical Aspects of Processes with Long-Range Memory, M. Courbage

About the Series

Chapman & Hall/CRC Research Notes in Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Differential Equations
MATHEMATICS / Functional Analysis
SCIENCE / Mathematical Physics