Gibbs Semigroups
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Topics In The Theory Of Gibbs Semigroups
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Author : Valentin Zagrebnov
language : en
Publisher: Leuven University Press
Release Date : 2003
Topics In The Theory Of Gibbs Semigroups written by Valentin Zagrebnov and has been published by Leuven University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
One-parameter semigroup theory started to be an important branch of mathematics in the thirties when it was realized that the theory has direct applications to partial differential equations, random processes, infinite dimensional control theory, mathematical physics, etc. It is now generally accepted as an integral part of contemporary functional analysis. Compact strongly continuous semigroups have been an important research subject since a long time, as in almost all applications of partial differential equations with bounded domains the semigroups turn out to be compact. From this point of view, the present volume of the Leuven Notes in Mathematical and Theoretical Physics emphasizes a special subclass of these semigroups. In fact, the focus here is mainly on semigroups acting on a Hilbert space H with values in the trace class ideal C1(H) of bounded operators on H. Historically, this class of semigroups is closely related to quantum statistical mechanics.
Gibbs Semigroups
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Author : Valentin A. Zagrebnov
language : en
Publisher: Springer Nature
Release Date : 2019-11-17
Gibbs Semigroups written by Valentin A. Zagrebnov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-17 with Mathematics categories.
This book focuses on the theory of the Gibbs semigroups, which originated in the 1970s and was motivated by the study of strongly continuous operator semigroups with values in the trace-class ideal. The book offers an up-to-date, exhaustive overview of the advances achieved in this theory after half a century of development. It begins with a tutorial introduction to the necessary background material, before presenting the Gibbs semigroups and then providing detailed and systematic information on the Trotter-Kato product formulae in the trace-norm topology. In addition to reviewing the state-of-art concerning the Trotter-Kato product formulae, the book extends the scope of exposition from the trace-class ideal to other ideals. Here, special attention is paid to results on semigroups in symmetrically normed ideals and in the Dixmier ideal. By examining the progress made in Gibbs semigroup theory and in extensions of the Trotter-Kato product formulae to symmetrically normed and Dixmier ideals, the book shares timely and valuable insights for readers interested in pursuing these subjects further. As such, it will appeal to researchers, undergraduate and graduate students in mathematics and mathematical physics.
Semigroups Of Linear Operators
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Author : David Applebaum
language : en
Publisher: Cambridge University Press
Release Date : 2019-08-15
Semigroups Of Linear Operators written by David Applebaum and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-15 with Mathematics categories.
Provides a graduate-level introduction to the theory of semigroups of operators.
Mathematical Analysis And Applications
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Author : Themistocles M. Rassias
language : en
Publisher: Springer Nature
Release Date : 2019-12-12
Mathematical Analysis And Applications written by Themistocles M. Rassias and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-12 with Mathematics categories.
An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.
Linear Operators And Their Spectra
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Author : E. Brian Davies
language : en
Publisher: Cambridge University Press
Release Date : 2007-04-26
Linear Operators And Their Spectra written by E. Brian Davies and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-26 with Mathematics categories.
This wide ranging but self-contained account of the spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt and trace class operators are discussed, as are one-parameter semigroups and perturbations of their generators. Two chapters are devoted to using these tools to analyze Markov semigroups. The text also provides a thorough account of the new theory of pseudospectra, and presents the recent analysis by the author and Barry Simon of the form of the pseudospectra at the boundary of the numerical range. This was a key ingredient in the determination of properties of the zeros of certain orthogonal polynomials on the unit circle. Finally, two methods, both very recent, for obtaining bounds on the eigenvalues of non-self-adjoint Schrodinger operators are described. The text concludes with a description of the surprising spectral properties of the non-self-adjoint harmonic oscillator.
Mathematical Analysis In Interdisciplinary Research
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Author : Ioannis N. Parasidis
language : en
Publisher: Springer Nature
Release Date : 2022-03-10
Mathematical Analysis In Interdisciplinary Research written by Ioannis N. Parasidis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-10 with Mathematics categories.
This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.
Xivth International Congress On Mathematical Physics
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Author : Jean-claude Zambrini
language : en
Publisher: World Scientific
Release Date : 2006-03-07
Xivth International Congress On Mathematical Physics written by Jean-claude Zambrini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-07 with Science categories.
In 2003 the XIV International Congress on Mathematical Physics (ICMP) was held in Lisbon with more than 500 participants. Twelve plenary talks were given in various fields of Mathematical Physics: E Carlen «On the relation between the Master equation and the Boltzmann Equation in Kinetic Theory»; A Chenciner «Symmetries and “simple” solutions of the classical n-body problem»; M J Esteban «Relativistic models in atomic and molecular physics»; K Fredenhagen «Locally covariant quantum field theory»; K Gawedzki «Simple models of turbulent transport»; I Krichever «Algebraic versus Liouville integrability of the soliton systems»; R V Moody «Long-range order and diffraction in mathematical quasicrystals»; S Smirnov «Critical percolation and conformal invariance»; J P Solovej «The energy of charged matter»; V Schomerus «Strings through the microscope»; C Villani «Entropy production and convergence to equilibrium for the Boltzmann equation»; D Voiculescu «Aspects of free probability».The book collects as well carefully selected invited Session Talks in: Dynamical Systems, Integrable Systems and Random Matrix Theory, Condensed Matter Physics, Equilibrium Statistical Mechanics, Quantum Field Theory, Operator Algebras and Quantum Information, String and M Theory, Fluid Dynamics and Nonlinear PDE, General Relativity, Nonequilibrium Statistical Mechanics, Quantum Mechanics and Spectral Theory, Path Integrals and Stochastic Analysis.
Trotter Kato Product Formul
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Author : Valentin A. Zagrebnov
language : en
Publisher: Springer Nature
Release Date : 2024-06-11
Trotter Kato Product Formul written by Valentin A. Zagrebnov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-11 with Mathematics categories.
The book captures a fascinating snapshot of the current state of results about the operator-norm convergent Trotter-Kato Product Formulæ on Hilbert and Banach spaces. It also includes results on the operator-norm convergent product formulæ for solution operators of the non-autonomous Cauchy problems as well as similar results on the unitary and Zeno product formulæ. After the Sophus Lie product formula for matrices was established in 1875, it was generalised to Hilbert and Banach spaces for convergence in the strong operator topology by H. Trotter (1959) and then in an extended form by T. Kato (1978). In 1993 Dzh. L. Rogava discovered that convergence of the Trotter product formula takes place in the operator-norm topology. The latter is the main subject of this book, which is dedicated essentially to the operator-norm convergent Trotter-Kato Product Formulæ on Hilbert and Banach spaces, but also to related results on the time-dependent, unitary and Zeno product formulæ. The book yields a detailed up-to-date introduction into the subject that will appeal to any reader with a basic knowledge of functional analysis and operator theory. It also provides references to the rich literature and historical remarks.
Proceedings Of The Xi International Conference Stochastic And Analytic Methods In Mathematical Physics
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Author : Boldrighini, Carlo
language : en
Publisher: Universitätsverlag Potsdam
Release Date : 2020
Proceedings Of The Xi International Conference Stochastic And Analytic Methods In Mathematical Physics written by Boldrighini, Carlo and has been published by Universitätsverlag Potsdam this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 – 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol’fovich Minlos, who passed away in January 2018. The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan. A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here.
Mathematical Results In Quantum Mechanics
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Author : Jaroslav Dittrich
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Mathematical Results In Quantum Mechanics written by Jaroslav Dittrich and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
At the age of almost three quarters of a century, quantum mechanics is by all accounts a mature theory. There were times when it seemed that it had borne its best fruit already and would give way to investigation of deeper levels of matter. Today this sounds like rash thinking. Modern experimental techniques have led to discoveries of numerous new quantum effects in solid state, optics and elsewhere. Quantum mechanics is thus gradually becoming a basis for many branches of applied physics, in this way entering our everyday life. While the dynamic laws of quantum mechanics are well known, a proper theoretical understanding requires methods which would allow us to de rive the abundance of observed quantum effects from the first principles. In many cases the rich structure hidden in the Schr6dinger equation can be revealed only using sophisticated tools. This constitutes a motivation to investigate rigorous methods which yield mathematically well-founded properties of quantum systems.