1st Edition

Generalized Functions, Operator Theory, and Dynamical Systems

By I Antoniou, G Lumer Copyright 1998
    392 Pages
    by Chapman & Hall

    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:

    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


    Ioannis Antoniou (Author) G. Lumer (Author)