Generalized Functions, Operator Theory, and Dynamical Systems /
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 formulat...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Chapman and Hall/CRC,
2021.
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| Edition: | 1st. |
| Series: | Chapman & Hall/CRC research notes in mathematics series ;
399 |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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. |
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| Item Description: | Part I: Generalized Functions and Operator Theory, An Introduction to Hyperfunctions and ?-expansions, Partial Inner Product Spaces of Analytic Functions, Rigged Spectral States: A Proclivity for Eigenvalues, Densities of Singular Measures and Generalized Spectral Decompositions, Convolution Kernels and Generalized Functions, Spectral Theory of Closed Linear Operators on Banach Spaces from a Locally Convex Point of View, Ultradistributions and the Levinson Condition, Representation of the Derivatives and Products of the Delta Function in Hilbert Space, Series Representations of the Complex Delta Function, Antieigenvalues: An Extended Spectral Theory, Part II: Operator Theory and Dynamical Systems Laws of Nature, Probability, and Time Symmetry Breaking, Extended Spectral Decompositions of Evolution Operators, Some Little Things About Rigged Hilbert Spaces and Quantum Mechanics and All That, Axiomatics of Thermodynamics and Quantum Chaos, Stochastic Evolution on Product Manifolds. Interaction Problems with Distributions and Hyperfunctions Data, Absolute Continuity of Convolutions of Singular Measures and New Branches of Spectrum of Liouvillians and Few-Body Hamiltonians, On Scattering Theories Involving Moving Boundaries, The Eigenvalue Problem for Networks of Beams Generalized Perturbations and Operator Relations, On Spectral Analysis of a Class of Integral-Difference Collision Operators, Dynamical Aspects of Processes with Long-Range Memory. |
| Physical Description: | 1 online resource (360 pages) |
| ISBN: | 9781000657746 1000657744 9780429332784 0429332785 9781000673463 1000673464 9781000665604 1000665607 |