Linear Functional Analysis

An Application-Oriented Introduction

Author: Hans Wilhelm Alt

Publisher: Springer

ISBN: 1447172809

Category: Mathematics

Page: 435

View: 8901

This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory. A complete introduction to the subject, Linear Functional Analysis will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.

Introduction to Functional Analysis

Author: Reinhold Meise,Dietmar Vogt

Publisher: Clarendon Press

ISBN: 0191590924


Page: 448

View: 6186

The book is written for students of mathematics and physics who have a basic knowledge of analysis and linear algebra. It can be used as a textbook for courses and/or seminars in functional analysis. Starting from metric spaces it proceeds quickly to the central results of the field, including the theorem of HahnBanach. The spaces (p Lp (X,(), C(X)' and Sobolov spaces are introduced. A chapter on spectral theory contains the Riesz theory of compact operators, basic facts on Banach and C*-algebras and the spectral representation for bounded normal and unbounded self-adjoint operators in Hilbert spaces. An introduction to locally convex spaces and their duality theory provides the basis for a comprehensive treatment of Fr--eacute--;chet spaces and their duals. In particular recent results on sequences spaces, linear topological invariants and short exact sequences of Fr--eacute--;chet spaces and the splitting of such sequences are presented. These results are not contained in any other book in this field.

Partielle Differentialgleichungen

Eine anwendungsorientierte Einführung

Author: Ben Schweizer

Publisher: Springer-Verlag

ISBN: 3662566680

Category: Mathematics

Page: 585

View: 9879

Das Buch führt in die Theorie der Partiellen Differentialgleichungen ein, lediglich die Grundvorlesungen der Analysis werden vorausgesetzt. Eine Vielzahl linearer und nichtlinearer Differentialgleichungen wird mit Modellierungsansätzen motiviert und rigoros analysiert. Nach den klassischen linearen Problemen der Potentialtheorie und Wärmeleitung werden insbesondere nichtlineare Probleme aus der Theorie poröser Medien, der Strömungsmechanik und der Festkörpermechanik behandelt. Entlang der Aufgabenstellungen von zunehmender Komplexität werden moderne Methoden und Theorien der Analysis entwickelt.​ In der vorliegenden 2. Auflage ist der Text überarbeitet und korrigiert, viele Zeichnungen sind verbessert, Anhang und Index sind erweitert.

Functional Analysis

Author: Walter Rudin

Publisher: Tata McGraw-Hill Education

ISBN: 9780070619883

Category: Functional analysis

Page: 424

View: 1074


Real and Functional Analysis

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461208971

Category: Mathematics

Page: 580

View: 1366

This book is meant as a text for a first-year graduate course in analysis. In a sense, it covers the same topics as elementary calculus but treats them in a manner suitable for people who will be using it in further mathematical investigations. The organization avoids long chains of logical interdependence, so that chapters are mostly independent. This allows a course to omit material from some chapters without compromising the exposition of material from later chapters.

From Fermat to Minkowski

Lectures on the Theory of Numbers and Its Historical Development

Author: W. Scharlau,H. Opolka

Publisher: Springer Science & Business Media

ISBN: 1475718675

Category: Mathematics

Page: 186

View: 5968

This book arose from a course of lectures given by the first author during the winter term 1977/1978 at the University of Münster (West Germany). The course was primarily addressed to future high school teachers of mathematics; it was not meant as a systematic introduction to number theory but rather as a historically motivated invitation to the subject, designed to interest the audience in number-theoretical questions and developments. This is also the objective of this book, which is certainly not meant to replace any of the existing excellent texts in number theory. Our selection of topics and examples tries to show how, in the historical development, the investigation of obvious or natural questions has led to more and more comprehensive and profound theories, how again and again, surprising connections between seemingly unrelated problems were discovered, and how the introduction of new methods and concepts led to the solution of hitherto unassailable questions. All this means that we do not present the student with polished proofs (which in turn are the fruit of a long historical development); rather, we try to show how these theorems are the necessary consequences of natural questions. Two examples might illustrate our objectives.

Functional analysis

Author: Harro Heuser

Publisher: John Wiley & Sons


Category: Mathematics

Page: 408

View: 7079


Linear Functional Analysis

Author: Joan Cerda

Publisher: American Mathematical Soc.

ISBN: 0821851152

Category: Mathematics

Page: 330

View: 3829

"Functional analysis studies the algebraic, geometric, and topological structures of spaces and operators that underlie many classical problems. Individual functions satisfying specific equations are replaced by classes of functions and transforms that are determined by the particular problems at hand. This book presents the basic facts of linear functional analysis as related to fundamental aspects of mathematical analysis and their applications. The exposition avoids unnecessary terminology and generality and focuses on showing how the knowledge of these structures clarifies what is essential in analytic problems. The material in the first part of the book can be used for an introductory course on functional analysis, with an emphasis on the role of duality. The second part introduces distributions and Sobolev spaces and their applications. Convolution and the Fourier transform are shown to be useful tools for the study of partial differential equations. Fundamental solutions and Green's functions are considered and the theory is illustrated with several applications. In the last chapters, the Gelfand transform for Banach algebras is used to present the spectral theory of bounded and unbounded operators, which is then used in an introduction to the basic axioms of quantum mechanics. The presentation is intended to be accessible to readers whose backgrounds include basic linear algebra, integration theory, and general topology. Almost 240 exercises will help the reader in better understanding the concepts employed."--Publisher's description.

Banach Spaces for Analysts

Author: P. Wojtaszczyk

Publisher: Cambridge University Press

ISBN: 9780521566759

Category: Mathematics

Page: 382

View: 3605

This book is intended to be used with graduate courses in Banach space theory.

Mathematical Methods in Physics

Distributions, Hilbert Space Operators, and Variational Methods

Author: Philippe Blanchard,Erwin Bruening

Publisher: Springer Science & Business Media

ISBN: 1461200490

Category: Mathematics

Page: 471

View: 7186

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.

On the Power of Fuzzy Markup Language

Author: Giovanni Acampora,Vincenzo Loia,Chang-Shing Lee,Mei-Hui Wang

Publisher: Springer

ISBN: 3642354882

Category: Computers

Page: 188

View: 4198

One of the most successful methodology that arose from the worldwide diffusion of Fuzzy Logic is Fuzzy Control. After the first attempts dated in the seventies, this methodology has been widely exploited for controlling many industrial components and systems. At the same time, and very independently from Fuzzy Logic or Fuzzy Control, the birth of the Web has impacted upon almost all aspects of computing discipline. Evolution of Web, Web2.0 and Web 3.0 has been making scenarios of ubiquitous computing much more feasible; consequently information technology has been thoroughly integrated into everyday objects and activities. What happens when Fuzzy Logic meets Web technology? Interesting results might come out, as you will discover in this book. Fuzzy Mark-up Language is a son of this synergistic view, where some technological issues of Web are re-interpreted taking into account the transparent notion of Fuzzy Control, as discussed here. The concept of a Fuzzy Control that is conceived and modeled in terms of a native web wisdom represents another step towards the last picture of Pervasive Web Intelligence.

Photochemistry and Photophysics of Coordination Compounds II

Author: Vincenzo Balzani,Sebastiano Campagna

Publisher: Springer

ISBN: 3540733493

Category: Science

Page: 327

View: 6588

Photochemistry (a term that broadly speaking includes photophysics) is abranchofmodernsciencethatdealswiththeinteractionoflightwithmatter and lies at the crossroadsof chemistry, physics, and biology. However, before being a branch of modern science, photochemistry was (and still is today), an extremely important natural phenomenon. When God said: “Let there be light”, photochemistry began to operate, helping God to create the world as wenowknowit.Itislikelythatphotochemistrywasthesparkfortheoriginof life on Earth and played a fundamental role in the evolution of life. Through the photosynthetic process that takes place in green plants, photochemistry is responsible for the maintenance of all living organisms. In the geological past photochemistry caused the accumulation of the deposits of coal, oil, and naturalgasthat wenowuseasfuels.Photochemistryisinvolved inthecontrol ofozoneinthestratosphereandinagreatnumber ofenvironmentalprocesses thatoccurintheatmosphere,inthesea,andonthesoil.Photochemistryisthe essenceoftheprocessofvisionandcausesavarietyofbehavioralresponsesin living organisms. Photochemistry as a science is quite young; we only need to go back less than one century to ?nd its early pioneer [1]. The concept of coordination compound is also relatively young; it was established in 1892, when Alfred Werner conceived his theory of metal complexes [2]. Since then, the terms coordination compound and metal complex have been used as synonyms, even if in the last 30 years, coordination chemistry has extended its scope to the binding ofall kinds of substrates [3, 4].


Author: Giancarlo Bernacchi


ISBN: 1326292536

Category: Science

Page: 218

View: 1007

-- New January 2018 REVISED RELEASE -- A friendly and non-formal approach to a subject of abstract mathematics that has important applications in physics, especially in General Relativity, but also in other fields. The purpose of the book is mainly dida

Advanced Techniques in Diagnostic Microbiology

Volume 1: Techniques

Author: Yi-Wei Tang,Charles W. Stratton

Publisher: Springer

ISBN: 3319339001

Category: Medical

Page: 541

View: 2406

In recent years, advanced molecular techniques in diagnostic microbiology have been revolutionizing the practice of clinical microbiology in the hospital setting. Molecular diagnostic testing in general and nucleic acid-based amplification methods in particular have been heralded as diagnostic tools for the new millennium. This third edition covers not only the most recent updates and advances, but details newly invented omic techniques, such as next generation sequencing. It is divided into two distinct volumes, with Volume 1 describing the techniques, and Volume 2 addressing their applications in the field. In addition, both volumes focus more so on the clinical relevance of the test results generated by these techniques than previous editions.

Nonlinear Spectral Theory

Author: Jürgen Appell,Espedito De Pascale,Alfonso Vignoli

Publisher: Walter de Gruyter

ISBN: 3110199262

Category: Mathematics

Page: 419

View: 860

In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear spectral theory. The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving.

Mathematical Methods

Linear Algebra / Normed Spaces / Distributions / Integration

Author: Jacob Korevaar

Publisher: Elsevier

ISBN: 1483270742

Category: Mathematics

Page: 518

View: 5138

Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions. The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector spaces, and delta sequences and convergence and approximation. The text then examines the Lebesgue integral, including approximation of integrable functions and applications, integration of sequences and series, functions of bounded variation and the Stieltjes integral, and multiple integrals. Curves and integrals, holomorphic functions and integrals in the complex plane, and multiple integrals are also discussed. The book is a valuable reference for students in the physical sciences, mathematics students interested in applications, and mathematically oriented engineering students.

Brain Theory From A Circuits And Systems Perspective

How Electrical Science Explains Neuro-circuits, Neuro-systems, and Qubits

Author: John Robert Burger

Publisher: Springer Science & Business Media

ISBN: 1461464129

Category: Medical

Page: 227

View: 9574

This book models an idealized neuron as being driven by basic electrical elements, the goal being to systematically characterize the logical properties of neural pulses. In order to constitute a system, neurons as pulsating devices may be represented using novel circuit elements as delineated in this book. A plausible brain system is implied by the delineated elements and logically follows from known and likely properties of a neuron. New to electrical science are novel pulse-related circuit elements involving recursive neurons. A recursive neuron, when properly excited, produces a self-sustaining pulse train that when sampled, provides a true output with a specified probability, and a false output with complementary probability. Because of its similarity to the qubits of quantum mechanics, the recursive pulsating neuron is termed a simulated qubit. Recursive neurons easily function as controlled toggle devices and so are capable of massively parallel calculations, this being a new dimension in brain functioning as described in this book. Simulated qubits and their possibilities are compared to the qubits of quantum physics. Included in the book are suggested neural circuits for associative memory search via a randomized process of cue selection, and neural circuits for priority calculations. These serve to select returns from long term memory, which in turn determines one's next conscious thought or action based on past memorized experiences. The book reports on proposals involving electron tunneling between synapses, and quantum computations within neurons. Although not a textbook, there are easy exercises at the ends of chapters, and in the appendix there are twelve simulation experiments concerning neurons. ​

Aeronomy of the Earth's Atmosphere and Ionosphere

Author: Mangalathayil Ali Abdu,Dora Pancheva

Publisher: Springer Science & Business Media

ISBN: 9789400703261

Category: Science

Page: 480

View: 1421

This book is a multi-author treatise on the most outstanding research problems in the field of the aeronomy of the Earth’s atmosphere and ionosphere, encompassing the science covered by Division II of the International Association of Geomagnetism and Aeronomy (IAGA). It contains several review articles and detailed papers by leading scientists in the field. The book is organized in five parts: 1) Mesosphere-Lower Thermosphere Dynamics and Chemistry; 2) Vertical Coupling by Upward Propagating Waves; 3) Ionospheric Electrodynamics and Structuring; 4) Thermosphere- Ionosphere Coupling, Dynamics and Trends and 5) Ionosphere-Thermosphere Disturbances and Modeling. The book consolidates the progress achieved in the field in recent years and it serves as a useful reference for graduate students as well as experienced researchers.