1.

Record Nr.

UNINA9910254293003321

Autore

Einsiedler Manfred

Titolo

Functional Analysis, Spectral Theory, and Applications / / by Manfred Einsiedler, Thomas Ward

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017

ISBN

3-319-58540-1

Edizione

[1st ed. 2017.]

Descrizione fisica

1 online resource (XIV, 614 p. 33 illus.)

Collana

Graduate Texts in Mathematics, , 2197-5612 ; ; 276

Classificazione

46

Disciplina

515.7

Soggetti

Functional analysis

Differential equations

Harmonic analysis

Number theory

Dynamics

Functional Analysis

Differential Equations

Abstract Harmonic Analysis

Number Theory

Dynamical Systems

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

Motivation -- Norms and Banach Spaces -- Hilbert Spaces, Fourier Series, Unitary Representations -- Uniform Boundedness and Open Mapping Theorem -- Sobolev Spaces and Dirichlet’s Boundary Problem -- Compact Self-Adjoint Operators, Laplace Eigenfunctions -- Dual Spaces -- Locally Convex Vector Spaces -- Unitary Operators and Flows, Fourier Transform -- Locally Compact Groups, Amenability, Property (T) -- Banach Algebras and the Spectrum -- Spectral Theory and Functional Calculus -- Self-Adjoint and Symmetric Operators -- The Prime Number Theorem -- Appendix A: Set Theory and Topology -- Appendix B: Measure Theory -- Hints for Selected Problems -- Notes. .

Sommario/riassunto

This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory.



In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study. Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics.

2.

Record Nr.

UNINA9910967805803321

Autore

Rescher Nicholas

Titolo

On explaining existence / / Nicholas Rescher

Pubbl/distr/stampa

Frankfurt, : Ontos Verlag, 2013

ISBN

3-86838-177-5

3-11-032044-4

Descrizione fisica

1 online resource (144 p.)

Disciplina

111.1

Soggetti

Ontology

Philosophy

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Frontmatter -- Table of Contents -- Preface -- Chapter One. EXISTENCE EXPLANATION AND THE HUME-EDWARDS PRINCIPLE -- Chapter Two. THE METAPHYSICS OF POSSIBILITY ACTUALIZATION -- Chapter Three. OPTIMALISM AND THE AXIOLOGICAL TURN -- Chapter Four. THE PIVOTAL ROLE OF INTELLIGENCE -- Chapter Five. DEFENDING OPTIMALISM -- Chapter Six. ON THE IMPROVABILITY OF THE WORLD -- Chapter Seven. OPTIMALISM AND THEISM -- Chapter Eight. ULTIMATE EXPLANATION -- NAME INDEX



Sommario/riassunto

No short book on the explanation of existence can afford the hubris of claiming to accomplish this task. And certainly no such claim can be or is being made here. What is at issue is not-and cannot be-an actual explanation. Rather, what is attempted here is at the very most a rough sketch of the conceptual architecture that an adequate explanation can be expected to exhibit. No more is achieved than a rough and general indication of the direction in which a satisfactory explanation can unfold. A vast amount of detail will have to be filled in to provide a tenable explanation. Only the rough shape that the explanation will have to take is something that one can map out in the basis of considerations of general principles, giving reasons why alternative directions are less promising and how objection to the indicated direction can be removed or mitigated. But the move from a general direction to a specific and detailed pathway calls for more than is-or can be-attempted here.