Category: Functional Analysis

By Jan Prüss

ISBN-10: 3034804989

ISBN-13: 9783034804981

This ebook offers with evolutionary platforms whose equation of nation may be formulated as a linear Volterra equation in a Banach area. the most function of the kernels concerned is they include unbounded linear operators. the purpose is a coherent presentation of the nation of artwork of the speculation together with unique proofs and its purposes to difficulties from mathematical physics, similar to viscoelasticity, warmth conduction, and electrodynamics with reminiscence. the significance of evolutionary necessary equations ‒ which shape a bigger classification than do evolution equations​ ‒ stems from such purposes and hence distinctive emphasis is put on those. a few versions are derived and, by way of the built thought, mentioned completely. An annotated bibliography containing 450 entries raises the book’s worth as an incisive reference textual content. --- this wonderful e-book provides a normal method of linear evolutionary platforms, with an emphasis on infinite-dimensional structures with time delays, comparable to these taking place in linear viscoelasticity without or with thermal results. It provides a truly typical and mature extension of the standard semigroup method of a extra common type of infinite-dimensional evolutionary platforms. this can be the 1st visual appeal within the kind of a monograph of this lately constructed conception. a considerable a part of the consequences are as a result of the writer, or are even new. (…) it isn't a e-book that one reads in a number of days. fairly, it may be regarded as an funding with lasting price. (Zentralblatt MATH) during this e-book, the writer, who has been on the leading edge of study on those difficulties for the decade, has amassed, and in lots of areas prolonged, the identified concept for those equations. furthermore, he has supplied a framework that enables one to narrate and evaluation varied ends up in the literature. (Mathematical reports) This ebook constitutes a hugely precious addition to the present literature at the thought of Volterra (evolutionary) quintessential equations and their purposes in physics and engineering. (…) and for the 1st time the tension is at the infinite-dimensional case. (SIAM Reviews)

By A. F. Timan

ISBN-10: 0080099297

ISBN-13: 9780080099293

Concept of Approximation of services of a true Variable discusses a few primary components of the trendy idea of approximation of services of a true variable. the cloth is grouped round the challenge of the relationship among the easiest approximation of capabilities to their structural properties.

This textual content consists of 8 chapters that spotlight the connection among some of the structural homes of genuine capabilities and the nature of attainable approximations to them via polynomials and different capabilities of easy development. every one bankruptcy concludes with a piece containing numerous difficulties and theorems, which complement the most textual content. the 1st chapters take on the Weierstrasss theorem, the simplest approximation via polynomials on a finite phase, and a few compact periods of services and their structural homes. the following chapters describe a few houses of algebraic polynomials and transcendental critical features of exponential style, in addition to the direct theorems of the optimistic concept of capabilities. those themes are by way of discussions of differential and positive features of communicate theorems. the ultimate chapters discover different theorems connecting the easiest approximations capabilities with their structural homes. those chapters additionally take care of the linear procedures of approximation of capabilities by means of polynomials.

The ebook is meant for post-graduate scholars and for mathematical scholars taking complicated classes, in addition to to staff within the box of the speculation of services.

By M. L. Agranovskii

ISBN-10: 0821846043

ISBN-13: 9780821846049

This ebook reports translation-invariant functionality areas and algebras on homogeneous manifolds. The critical subject is the connection among the homogeneous constitution of a manifold and the category of translation-invariant functionality areas and algebras at the manifold. Agranovskiĭ obtains classifications of translation-invariant areas and algebras of services on semisimple and nilpotent Lie teams, Riemann symmetric areas, and bounded symmetric domain names. whilst such classifications are attainable, they lead in lots of instances to new characterizations of the classical functionality areas, from the viewpoint in their workforce of admissible alterations of variable. The algebra of holomorphic services performs an important position in those classifications whilst a homogeneous complicated or CR-structure exists at the manifold. This results in new characterizations of holomorphic services and their boundary values for one- and multidimensional advanced domains.

Readership: experts in practical research, harmonic research, functionality idea of 1 and a number of other advanced variables, and Lie crew illustration.

By Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov

ISBN-10: 0387855866

ISBN-13: 9780387855868

ISBN-10: 0387855882

ISBN-13: 9780387855882

The goal of this ebook is to offer a latest account of mapping idea with emphasis on quasiconformal mapping and its generalizations. The modulus approach used to be initiated through Arne Beurling and Lars Ahlfors to check conformal mappings, and later this system used to be prolonged and improved by way of a number of others. The recommendations are geometric they usually have became out to be an vital instrument within the learn of quasiconformal and quasiregular mappings in addition to their generalizations. The booklet relies on fresh learn papers and extends the modulus approach past the classical purposes of the modulus innovations awarded in lots of monographs.

By Rene Erlin Castillo, Humberto Rafeiro

ISBN-10: 3319300326

ISBN-13: 9783319300320

ISBN-10: 3319300342

ISBN-13: 9783319300344

Introduces reader to fresh subject matters in areas of measurable functions
Includes component of difficulties on the finish of every bankruptcy ​
Content allows use with mixed-level classes
Includes non-standard functionality areas, viz. variable exponent Lebesgue areas and grand Lebesgue spaces

This booklet is dedicated solely to Lebesgue areas and their direct derived areas. particular in its sole commitment, this booklet explores Lebesgue areas, distribution services and nonincreasing rearrangement. furthermore, it additionally bargains with vulnerable, Lorentz and the more moderen variable exponent and grand Lebesgue areas with massive aspect to the proofs. The publication additionally touches on simple harmonic research within the aforementioned areas. An appendix is given on the finish of the booklet giving it a self-contained personality. This paintings is perfect for academics, graduate scholars and researchers.

Topics
Abstract Harmonic Analysis
Functional research

By Jürgen Elstrodt

ISBN-10: 3642179045

ISBN-13: 9783642179044

Dieses Lehrbuch der Maß- und Integrationstheorie vermittelt dem Leser ein solides Basiswissen, wie es für weite Bereiche der Mathematik unerläßlich ist, insbesondere für reelle research, Funktionalanalysis, Wahrscheinlichkeitstheorie und mathematische Statistik. Thematische Schwerpunkte sind Produktmaße, Fourier-Transformation, Transformationsformel, Konvergenzbegriffe, absolute Stetigkeit und Maße auf topologischen Räumen. Höhepunkte sind die Herleitung des Rieszschen

Darstellungssatzes mit Hilfe eines Fortsetzungsresultats von Kisy´nski und der Beweis der Existenz und Eindeutigkeit des Haarschen Maßes. Ferner enthält das Buch einen Abschnitt über Konvergenz von Maßen und den Satz von Prochorov. Der textual content wird aufgelockert durch mathematikhistorische Ausflüge und Kurzporträts von Mathematikern, die zum Thema des Buches wichtige Beiträge geliefert haben. Eine Vielzahl von Übungsaufgaben vertieft den Stoff.

Aus den Rezensionen:
„ …In diesem Buch wird die Maß- und Integrationstheorie als ein zentrales Gebiet der Mathematik dargestellt, das insbesondere für die Funktionalanalysis und die Stochastik unentbehrlich ist; es hat daher zu Recht seinen Platz in der Reihe ‘Grundwissen Mathematik’. Vor allem für denjenigen, der über Grundkenntnisse bereits verfügt, ist es eine Quelle der Anregung und Bereicherung.“
(Zentralblatt für Mathematik und ihre Grenzgebiete 861 (1997), 148–149)

„ …Das Buch …zeugt von großer Lehrerfahrung des Autors. Es ist flüssig geschrieben, vermittelt solides Grundwissen und enthält viele Beispiele und Übungsaufgaben. Deshalb kann ich es Mathematik-Studenten aller Richtungen (einschließlich Lehramtskandidaten) zum Gebrauch neben der Vorlesung nachdrücklich empfehlen.“
(Zeitschrift für research und ihre Anwendungen 16 (1997), 493–49

By Rajendra Bhatia

ISBN-10: 8185931895

ISBN-13: 9788185931890

Those notes are a checklist of a one semester direction on practical research given by means of the writer to moment 12 months grasp of facts scholars on the Indian Statistical Institute, New Delhi. scholars taking this path have a robust historical past in genuine research, linear algebra, degree idea and chance, and the direction proceeds quickly from the definition of a normed linear area to the spectral theorem for bounded selfadjoint operators in a Hilbert area. The ebook is organised as twenty six lectures, each one similar to a 90 minute category consultation. this can be useful to lecturers making plans a path in this subject. organized scholars can learn it all alone.

By Antonio Ambrosetti, David Arcoya Álvarez

ISBN-10: 0817681132

ISBN-13: 9780817681135

This self-contained textbook offers the fundamental, summary instruments utilized in nonlinear research and their purposes to semilinear elliptic boundary price difficulties. via first outlining the benefits and downsides of every process, this complete textual content monitors how quite a few ways can simply be utilized to a number version cases.

An advent to Nonlinear useful research and Elliptic Problems is split into components: the 1st discusses key effects akin to the Banach contraction precept, a set element theorem for expanding operators, neighborhood and worldwide inversion conception, Leray–Schauder measure, serious element thought, and bifurcation thought; the second one half exhibits how those summary effects follow to Dirichlet elliptic boundary worth difficulties. The exposition is pushed via quite a few prototype difficulties and exposes quite a few methods to fixing them.

Complete with a initial bankruptcy, an appendix that incorporates extra effects on susceptible derivatives, and chapter-by-chapter routines, this booklet is a realistic textual content for an introductory direction or seminar on nonlinear sensible analysis.

By Ryan Alvarado, Marius Mitrea

ISBN-10: 3319181319

ISBN-13: 9783319181318

ISBN-10: 3319181327

ISBN-13: 9783319181325

Systematically developing an optimum idea, this monograph develops and explores a number of methods to Hardy areas within the atmosphere of Alhlfors-regular quasi-metric areas. The textual content is split into major elements, with the 1st half supplying atomic, molecular, and grand maximal functionality characterizations of Hardy areas and formulates sharp models of simple analytical instruments for quasi-metric areas, comparable to a Lebesgue differentiation theorem with minimum calls for at the underlying degree, a maximally tender approximation to the id and a Calderon-Zygmund decomposition for distributions. those effects are of autonomous curiosity. the second one half establishes very common standards ensuring linear operator acts continually from a Hardy house right into a topological vector area, emphasizing the function of the motion of the operator on atoms. functions contain the solvability of the Dirichlet challenge for elliptic structures within the upper-half house with boundary facts from Hardy areas. The instruments confirmed within the first half are then used to boost a pointy conception of Besov and Triebel-Lizorkin areas in Ahlfors-regular quasi-metric areas. The monograph is essentially self-contained and is meant for mathematicians, graduate scholars and execs with a mathematical historical past who're attracted to the interaction among research and geometry.