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Functional Calculus
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Book Synopsis Concrete Functional Calculus by : R. M. Dudley
Download or read book Concrete Functional Calculus written by R. M. Dudley and published by Springer Science & Business Media. This book was released on 2010-11-03 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients. In this book existence and uniqueness of solutions are proved under suitable assumptions for nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation. Key features and topics: Extensive usage of p-variation of functions, and applications to stochastic processes. This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability.
Author :Prof. Fabrizio Colombo Politecnico di Milano Publisher :Springer Science & Business Media ISBN 13 :3034801106 Total Pages :228 pages Book Rating :4.0/5 (348 download)
Book Synopsis Noncommutative Functional Calculus by : Prof. Fabrizio Colombo Politecnico di Milano
Download or read book Noncommutative Functional Calculus written by Prof. Fabrizio Colombo Politecnico di Milano and published by Springer Science & Business Media. This book was released on 2011-03-18 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a functional calculus for n-tuples of not necessarily commuting linear operators. In particular, a functional calculus for quaternionic linear operators is developed. These calculi are based on a new theory of hyperholomorphicity for functions with values in a Clifford algebra: the so-called slice monogenic functions which are carefully described in the book. In the case of functions with values in the algebra of quaternions these functions are named slice regular functions. Except for the appendix and the introduction all results are new and appear for the first time organized in a monograph. The material has been carefully prepared to be as self-contained as possible. The intended audience consists of researchers, graduate and postgraduate students interested in operator theory, spectral theory, hypercomplex analysis, and mathematical physics.
Book Synopsis The Functional Calculus for Sectorial Operators by : Markus Haase
Download or read book The Functional Calculus for Sectorial Operators written by Markus Haase and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.
Book Synopsis An Introduction to Functional Programming Through Lambda Calculus by : Greg Michaelson
Download or read book An Introduction to Functional Programming Through Lambda Calculus written by Greg Michaelson and published by Courier Corporation. This book was released on 2011-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-respected text offers an accessible introduction to functional programming concepts and techniques for students of mathematics and computer science. The treatment is as nontechnical as possible, assuming no prior knowledge of mathematics or functional programming. Numerous exercises appear throughout the text, and all problems feature complete solutions. 1989 edition.
Book Synopsis Functional Calculus by : Arvind P Vidhyarthi
Download or read book Functional Calculus written by Arvind P Vidhyarthi and published by Lulu.com. This book was released on 2015-09-19 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional Calculus is a part of calculus and also reference book for college & engineering.
Book Synopsis Functional Fractional Calculus by : Shantanu Das
Download or read book Functional Fractional Calculus written by Shantanu Das and published by Springer Science & Business Media. This book was released on 2011-06-01 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ‘ordinary’ calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the ‘solvable’ system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving ‘approximately exact’ series solutions. Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, “...the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.” This XXI century has thus started to ‘think-exactly’ for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.
Book Synopsis Hilbert Space Operators in Quantum Physics by : Jirí Blank
Download or read book Hilbert Space Operators in Quantum Physics written by Jirí Blank and published by Springer Science & Business Media. This book was released on 2008-09-24 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.
Book Synopsis Functional Analysis, Calculus of Variations and Optimal Control by : Francis Clarke
Download or read book Functional Analysis, Calculus of Variations and Optimal Control written by Francis Clarke and published by Springer Science & Business Media. This book was released on 2013-02-06 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.
Book Synopsis Functional Calculi by : Charles W Swartz
Download or read book Functional Calculi written by Charles W Swartz and published by World Scientific. This book was released on 2013-03-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, i.e. a method for defining “functions of an operator”. Perhaps the most familiar example is based on the spectral theorem for bounded self-adjoint operators on a complex Hilbert space.This book contains an exposition of several such functional calculi. In particular, there is an exposition based on the spectral theorem for bounded, self-adjoint operators, an extension to the case of several commuting self-adjoint operators and an extension to normal operators. The Riesz operational calculus based on the Cauchy integral theorem from complex analysis is also described. Finally, an exposition of a functional calculus due to H. Weyl is given.
Book Synopsis Functional Calculi by : Carlos Bosch Giral
Download or read book Functional Calculi written by Carlos Bosch Giral and published by World Scientific Publishing Company Incorporated. This book was released on 2013 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, i.e. a method for defining "functions of an operator." Perhaps the most familiar example is based on the spectral theorem for bounded self-adjoint operators on a complex Hilbert space. This book contains an exposition of several such functional calculi. In particular, there is an exposition based on the spectral theorem for bounded, self-adjoint operators, an extension to the case of several commuting self-adjoint operators and an extension to normal operators. The Riesz operational calculus based on the Cauchy integral theorem from complex analysis is also described. Finally, an exposition of a functional calculus due to H. Weyl is given.
Book Synopsis A Course in Functional Analysis by : John B Conway
Download or read book A Course in Functional Analysis written by John B Conway and published by Springer. This book was released on 2019-03-09 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excellent text for a first graduate course in functional analysis....Many interesting and important applications are included....It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author." --MATHEMATICAL REVIEWS
Book Synopsis The Calculus of Variations and Functional Analysis by : L. P. Lebedev
Download or read book The Calculus of Variations and Functional Analysis written by L. P. Lebedev and published by World Scientific. This book was released on 2003 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is aimed at those who are concerned about Chinese medicine - how it works, what its current state is and, most important, how to make full use of it. The audience therefore includes clinicians who want to serve their patients better and patients who are eager to supplement their own conventional treatment. The authors of the book belong to three different fields, modern medicine, Chinese medicine and pharmacology. They provide information from their areas of expertise and concern, attempting to make it comprehensive for users. The approach is macroscopic and philosophical; readers convinced of the philosophy are to seek specific assistance.
Book Synopsis Advanced Calculus (Revised Edition) by : Lynn Harold Loomis
Download or read book Advanced Calculus (Revised Edition) written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Download or read book Functional Calculus written by Kamal Shah and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Functional Calculus for Subnormal Operators II by : John B. Conway
Download or read book A Functional Calculus for Subnormal Operators II written by John B. Conway and published by American Mathematical Soc.. This book was released on 1977 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let S be a subnormal operator on a Hilbert space [script]H with minimal normal extension [italic]N operating on [italic]K, and let [lowercase Greek]Mu be a scalar valued spectral measure for [italic]N. If [italic]P[infinity symbol]([lowercase Greek]Mu) denotes the weak star closure of the polynomials in [italic]L[infinity symbol]([lowercase Greek]Mu) = [italic]L1[infinity symbol]([lowercase Greek]Mu) then for [script]f in [italic]P[infinity symbol]([lowercase Greek]Mu) it follows that [script]f([italic]N) leaves [script]H invariant; if [script]f([italic]S) is defined as the restriction of [script]f([italic]N) to [script]H then a functional calculus for [italic]S is obtained. This functional calculus is investigated in this paper.
Book Synopsis Completing the Riesz-Dunford Functional Calculus by : John B. Conway
Download or read book Completing the Riesz-Dunford Functional Calculus written by John B. Conway and published by American Mathematical Soc.. This book was released on 1989 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let [script lowercase]f be any analytic function defined in a neighborhood of the non-empty set [italic]E and let [script]S([italic]E) denote the set of all operator having spectrum included in [italic]E. In this paper the closure and interior of the set [script lowercase]f([script]S([italic]E)) [identical equality] {[script lowercase]f([italic]A): [italic]A [set membership] [script]S([italic]E)} are characterized. Some applications serve to illustrate the interplay between the analyticity of the functions and the spectral behavior of the operators.
Book Synopsis Functional Calculi by : Carlos Bosch
Download or read book Functional Calculi written by Carlos Bosch and published by World Scientific. This book was released on 2013 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, i.e. a method for defining OC functions of an operatorOCO. Perhaps the most familiar example is based on the spectral theorem for bounded self-adjoint operators on a complex Hilbert space.This book contains an exposition of several such functional calculi. In particular, there is an exposition based on the spectral theorem for bounded, self-adjoint operators, an extension to the case of several commuting self-adjoint operators and an extension to normal operators. The Riesz operational calculus based on the Cauchy integral theorem from complex analysis is also described. Finally, an exposition of a functional calculus due to H. Weyl is given.
