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Title:Ideal Spaces
Format Type:Ebook
Author:
Publisher:Springer
ISBN:3540631607
ISBN 13:
Number of Pages:150
Category:Manga

Ideal Spaces by Martin Väth

PDF, EPUB, MOBI, TXT, DOC Ideal Spaces Ideal spaces are a very general class of normed spaces of measurable functions which includes e g Lebesgue and Orlicz spaces Their most important application is in functional analysis in the theory of usual and partial integral and integro differential equations The book is a rather complete and self contained introduction into the general theory of ideal spaces Some emphasis is put on spaces of vector valued functions and on the constructive viewpoint of the theory without the axiom of choice The reader should have basic knowledge in functional analysis and measure theory

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Integration Theory - A Second Course, Nonstandard Analysis, Elemente der Funktionalanalysis: Vektorrume, Operatoren und Fixpunktstze, Ideal Spaces, Volterra and Integral Equations of Vector Functions
Dies ist das erste Lehrbuch das eine elementare Einfuhrung sowohl in die Lineare als auch in die Nichtlineare Analysis gibt und viele Wechselwirkungen zwischen beiden diskutiert Ein besonderer Vorteil des Buches liegt auch darin dass es oft von Beispielen und Gegenbeispielen ausgeht nicht von abstrakten Uberlegungen br br Contents br Normierte lineare Raume Kompakte Mengen Kompaktheitskriterien Beschrankte lineare Operatoren Kompakte Operatoren Matrixoperatoren und Integraloperatoren Fredholm Alternative Losbarkeit linearer Gleichungen Nichtlineare Operatoren Banachscher Fixpunktsatz Brouwerscher Fixpunktsatz Schauderscher Fixpunktsatz Darboscher Fixpunktsatz Losbarkeit nichtlinearer Gleichungen, This book introduces Robinson s nonstandard analysis an application of model theory in analysis Unlike some texts it does not attempt to teach elementary calculus on the basis of nonstandard analysis but points to some applications in more advanced analysis The contents proceed from a discussion of the preliminaries to Nonstandard Models Nonstandard Real Analysis Enlargements and Saturated Models Functionals Generalized Limits and Additive Measures and finally Nonstandard Topology and Functional Analysis No background in model theory is required although some familiarity with analysis topology or functional analysis is useful This self contained book can be understood after a basic calculus course, This book presents a general approach to integration theory as well as some advanced topics It includes some new results but is also a self contained introduction suitable for a graduate student doing self study or for an advanced course on integration theory The book is divided into two parts In the first part integration theory is developed from the start in a general setting and immediately for vector valued functions This material can hardly be found in other textbooks The second part covers various topics related to integration theory such as spaces of measurable functions convolutions famous paradoxes and extensions of formulae from elementary calculus to the setting of the Lebesgue integral, Develops and applies topological and algebraic methods to study abstract Volterra operators and differential equations arising in models for real world phenomena in physics biology and a host of other disciplines Presents completely new results that appear in book form for the first time