Download or read book The Adjoint of a Semigroup of Linear Operators written by Jan van Neerven and published by Springer. This book was released on 2006-11-15 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a systematic treatment of the abstract theory of adjoint semigroups. After presenting the basic elementary results, the following topics are treated in detail: The sigma (X, X )-topology, -reflexivity, the Favard class, Hille-Yosida operators, interpolation and extrapolation, weak -continuous semigroups, the codimension of X in X , adjoint semigroups and the Radon-Nikodym property, tensor products of semigroups and duality, positive semigroups and multiplication semigroups. The major part of the material is reasonably self-contained and is accessible to anyone with basic knowledge of semi- group theory and Banach space theory. Most of the results are proved in detail. The book is addressed primarily to researchers working in semigroup theory, but in view of the "Banach space theory" flavour of many of the results, it will also be of interest to Banach space geometers and operator theorists.

Download or read book Semigroups of Linear Operators written by David Applebaum and published by Cambridge University Press. This book was released on 2019-08-15 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a graduate-level introduction to the theory of semigroups of operators.

Download or read book Scattering Theory for Transport Phenomena written by Hassan Emamirad and published by Springer Nature. This book was released on 2021-06-27 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scattering theory for transport phenomena was initiated by P. Lax and R. Phillips in 1967. Since then, great progress has been made in the field and the work has been ongoing for more than half a century. This book shows part of that progress. The book is divided into 7 chapters, the first of which deals with preliminaries of the theory of semigroups and C*-algebra, different types of semigroups, Schatten–von Neuman classes of operators, and facts about ultraweak operator topology, with examples using wavelet theory. Chapter 2 goes into abstract scattering theory in a general Banach space. The wave and scattering operators and their basic properties are defined. Some abstract methods such as smooth perturbation and the limiting absorption principle are also presented. Chapter 3 is devoted to the transport or linearized Boltzmann equation, and in Chapter 4 the Lax and Phillips formalism is introduced in scattering theory for the transport equation. In their seminal book, Lax and Phillips introduced the incoming and outgoing subspaces, which verify their representation theorem for a dissipative hyperbolic system initially and also matches for the transport problem. By means of these subspaces, the Lax and Phillips semigroup is defined and it is proved that this semigroup is eventually compact, hence hyperbolic. Balanced equations give rise to two transport equations, one of which can satisfy an advection equation and one of which will be nonautonomous. For generating, the Howland semigroup and Howland’s formalism must be used, as shown in Chapter 5. Chapter 6 is the highlight of the book, in which it is explained how the scattering operator for the transport problem by using the albedo operator can lead to recovery of the functionality of computerized tomography in medical science. The final chapter introduces the Wigner function, which connects the Schrödinger equation to statistical physics and the Husimi distribution function. Here, the relationship between the Wigner function and the quantum dynamical semigroup (QDS) can be seen.

Download or read book The Asymptotic Behaviour of Semigroups of Linear Operators written by Jan van Neerven and published by Birkhäuser. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. The focus is on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator. The most recent developments in the field are included, such as the Arendt-Batty-Lyubich-Vu theorem, the spectral mapp- ing theorem of Latushkin and Montgomery-Smith, Weis's theorem on stability of positive semigroup in Lp-spaces, the stability theorem for semigroups whose resolvent is bounded in a half-plane, and a systematic theory of individual stability. Addressed to researchers and graduate students with interest in the fields of operator semigroups and evolution equations, this book is self-contained and provides complete proofs.

Download or read book Semigroups of Linear Operators and Applications to Partial Differential Equations written by Amnon Pazy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

Download or read book Markov Processes written by E. B. Dynkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modem theory of Markov processes has its origins in the studies of A. A. MARKOV (1906-1907) on sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian motion (L. BACHELlER 1900, A. EIN STEIN 1905). The first correct mathematical construction of a Markov process with continuous trajectories was given by N. WIENER in 1923. (This process is often called the Wiener process.) The general theory of Markov processes was developed in the 1930's and 1940's by A. N. KOL MOGOROV, W. FELLER, W. DOEBLlN, P. LEVY, J. L. DOOB, and others. During the past ten years the theory of Markov processes has entered a new period of intensive development. The methods of the theory of semigroups of linear operators made possible further progress in the classification of Markov processes by their infinitesimal characteristics. The broad classes of Markov processes with continuous trajectories be came the main object of study. The connections between Markov pro cesses and classical analysis were further developed. It has become possible not only to apply the results and methods of analysis to the problems of probability theory, but also to investigate analytic problems using probabilistic methods. Remarkable new connections between Markov processes and potential theory were revealed. The foundations of the theory were reviewed critically: the new concept of strong Markov process acquired for the whole theory of Markov processes great importance.

Download or read book Spectral Expansions of Non Self Adjoint Generalized Laguerre Semigroups written by Pierre Patie and published by American Mathematical Society. This book was released on 2021-11-16 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Co Semigroups and Applications written by Ioan I. Vrabie and published by Elsevier. This book was released on 2003-03-21 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications. There are several specialized, but quite interesting, topics which didn't find their place into a monograph till now, mainly because they are very new. So, the book, although containing the main parts of the classical theory of Co-semigroups, as the Hille-Yosida theory, includes also several very new results, as for instance those referring to various classes of semigroups such as equicontinuous, compact, differentiable, or analytic, as well as to some nonstandard types of partial differential equations, i.e. elliptic and parabolic systems with dynamic boundary conditions, and linear or semilinear differential equations with distributed (time, spatial) measures. Moreover, some finite-dimensional-like methods for certain semilinear pseudo-parabolic, or hyperbolic equations are also disscussed. Among the most interesting applications covered are not only the standard ones concerning the Laplace equation subject to either Dirichlet, or Neumann boundary conditions, or the Wave, or Klein-Gordon equations, but also those referring to the Maxwell equations, the equations of Linear Thermoelasticity, the equations of Linear Viscoelasticity, to list only a few. Moreover, each chapter contains a set of various problems, all of them completely solved and explained in a special section at the end of the book.The book is primarily addressed to graduate students and researchers in the field, but it would be of interest for both physicists and engineers. It should be emphasised that it is almost self-contained, requiring only a basic course in Functional Analysis and Partial Differential Equations.

Download or read book Functional Analysis and Semi groups written by Einar Hille and published by American Mathematical Soc.. This book was released on 1996-02-06 with total page 826 pages. Available in PDF, EPUB and Kindle. Book excerpt: Early in 1952 it became obvious that a new printing would be needed, and new advances in the theory called for extensive revision. It has been completely rewritten, mostly by Phillips, and much has been added while keeping the existing framework. Thus, the algebraic tools play a major role, and are introduced early, leading to a more satisfactory operational calculus and spectral theory. The Laplace-Stieltjes transform methods, used by Hille, have not been replaced but rather supplemented by the new tools. - Foreword.

Download or read book The Feynman Integral and Feynman s Operational Calculus written by Gerald W. Johnson and published by Clarendon Press. This book was released on 2000-03-16 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results.

Download or read book Fractional Order Equations and Inclusions written by Michal Fečkan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-11-07 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents fractional difference, integral, differential, evolution equations and inclusions, and discusses existence and asymptotic behavior of their solutions. Controllability and relaxed control results are obtained. Combining rigorous deduction with abundant examples, it is of interest to nonlinear science researchers using fractional equations as a tool, and physicists, mechanics researchers and engineers studying relevant topics. Contents Fractional Difference Equations Fractional Integral Equations Fractional Differential Equations Fractional Evolution Equations: Continued Fractional Differential Inclusions

Download or read book Positive Semigroups of Operators and Applications written by O. Bratteli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This means that semigroup theory may be applied directly to the study of the equation I'!.f = h on M. In [45] Yau proves that, for h ~ 0, there are no nonconstant, nonnegative solutions f in [j' for 1

Download or read book Quantized Number Theory Fractal Strings And The Riemann Hypothesis From Spectral Operators To Phase Transitions And Universality written by Hafedh Herichi and published by World Scientific. This book was released on 2021-07-27 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studying the relationship between the geometry, arithmetic and spectra of fractals has been a subject of significant interest in contemporary mathematics. This book contributes to the literature on the subject in several different and new ways. In particular, the authors provide a rigorous and detailed study of the spectral operator, a map that sends the geometry of fractal strings onto their spectrum. To that effect, they use and develop methods from fractal geometry, functional analysis, complex analysis, operator theory, partial differential equations, analytic number theory and mathematical physics.Originally, M L Lapidus and M van Frankenhuijsen 'heuristically' introduced the spectral operator in their development of the theory of fractal strings and their complex dimensions, specifically in their reinterpretation of the earlier work of M L Lapidus and H Maier on inverse spectral problems for fractal strings and the Riemann hypothesis.One of the main themes of the book is to provide a rigorous framework within which the corresponding question 'Can one hear the shape of a fractal string?' or, equivalently, 'Can one obtain information about the geometry of a fractal string, given its spectrum?' can be further reformulated in terms of the invertibility or the quasi-invertibility of the spectral operator.The infinitesimal shift of the real line is first precisely defined as a differentiation operator on a family of suitably weighted Hilbert spaces of functions on the real line and indexed by a dimensional parameter c. Then, the spectral operator is defined via the functional calculus as a function of the infinitesimal shift. In this manner, it is viewed as a natural 'quantum' analog of the Riemann zeta function. More precisely, within this framework, the spectral operator is defined as the composite map of the Riemann zeta function with the infinitesimal shift, viewed as an unbounded normal operator acting on the above Hilbert space.It is shown that the quasi-invertibility of the spectral operator is intimately connected to the existence of critical zeros of the Riemann zeta function, leading to a new spectral and operator-theoretic reformulation of the Riemann hypothesis. Accordingly, the spectral operator is quasi-invertible for all values of the dimensional parameter c in the critical interval (0,1) (other than in the midfractal case when c =1/2) if and only if the Riemann hypothesis (RH) is true. A related, but seemingly quite different, reformulation of RH, due to the second author and referred to as an 'asymmetric criterion for RH', is also discussed in some detail: namely, the spectral operator is invertible for all values of c in the left-critical interval (0,1/2) if and only if RH is true.These spectral reformulations of RH also led to the discovery of several 'mathematical phase transitions' in this context, for the shape of the spectrum, the invertibility, the boundedness or the unboundedness of the spectral operator, and occurring either in the midfractal case or in the most fractal case when the underlying fractal dimension is equal to ½ or 1, respectively. In particular, the midfractal dimension c=1/2 is playing the role of a critical parameter in quantum statistical physics and the theory of phase transitions and critical phenomena.Furthermore, the authors provide a 'quantum analog' of Voronin's classical theorem about the universality of the Riemann zeta function. Moreover, they obtain and study quantized counterparts of the Dirichlet series and of the Euler product for the Riemann zeta function, which are shown to converge (in a suitable sense) even inside the critical strip.For pedagogical reasons, most of the book is devoted to the study of the quantized Riemann zeta function. However, the results obtained in this monograph are expected to lead to a quantization of most classic arithmetic zeta functions, hence, further 'naturally quantizing' various aspects of analytic number theory and arithmetic geometry.The book should be accessible to experts and non-experts alike, including mathematics and physics graduate students and postdoctoral researchers, interested in fractal geometry, number theory, operator theory and functional analysis, differential equations, complex analysis, spectral theory, as well as mathematical and theoretical physics. Whenever necessary, suitable background about the different subjects involved is provided and the new work is placed in its proper historical context. Several appendices supplementing the main text are also included.

Download or read book Semigroups of Linear Operators and Applications written by Jerome A. Goldstein and published by Courier Dover Publications. This book was released on 2017-05-17 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced graduate-level treatment of semigroup theory explores semigroups of linear operators and linear Cauchy problems. The text features challenging exercises and emphasizes motivation, heuristics, and further applications. 1985 edition.

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Download or read book Perturbation theory for linear operators written by Tosio Kato and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book One Parameter Semigroups for Linear Evolution Equations written by Klaus-Jochen Engel and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory. Also, the book places an emphasis on philosophical motivation and the historical background.