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Functional equations. --- Associative law (Mathematics) --- Mathematical analysis. --- Functional equations --- Mathematical analysis --- Mathematics --- Equations, Functional --- Functional analysis --- 517.1 Mathematical analysis --- Study and teaching --- Harmonic analysis. Fourier analysis

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Assuming only a basic knowledge of functional analysis, the book gives the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. The aim of this text is to provide the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. Fernando Albiac received his PhD in 2000 from Universidad Publica de Navarra, Spain. He is currently Visiting Assistant Professor of Mathematics at the University of Missouri, Columbia. Nigel Kalton is Professor of Mathematics at the University of Missouri, Columbia. He has written over 200 articles with more than 82 different co-authors, and most recently, was the recipient of the 2004 Banach medal of the Polish Academy of Sciences.

Banach spaces --- Functions of complex variables --- Generalized spaces --- Topology --- Functional analysis. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations

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This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the p

Boundary value problems. --- Functional differential equations. --- Differential equations, Functional --- Differential equations --- Functional equations --- Boundary conditions (Differential equations) --- Functions of complex variables --- Mathematical physics --- Initial value problems

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Differential equations --- Boundary value problems --- 517.91 --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517.91 Differential equations --- Boundary conditions (Differential equations) --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Numerical solutions

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The present monograph deals with the functional calculus for unbounded operators in general and for sectorial operators in particular. Sectorial operators abound in the theory of evolution equations, especially those of parabolic type. They satisfy a certain resolvent condition that leads to a holomorphic functional calculus based on Cauchy-type integrals. Via an abstract extension procedure, this elementary functional calculus is then extended to a large class of (even meromorphic) functions. With this functional calculus at hand, the book elegantly covers holomorphic semigroups, fractional powers, and logarithms. Special attention is given to perturbation results and the connection with the theory of interpolation spaces. A chapter is devoted to the exciting interplay between numerical range conditions, similarity problems and functional calculus on Hilbert spaces. Two chapters describe applications, for example to elliptic operators, to numerical approximations of parabolic equations, and to the maximal regularity problem. This book is the first systematic account of a subject matter which lies in the intersection of operator theory, evolution equations, and harmonic analysis. It is an original and comprehensive exposition of the theory as a whole. Written in a clear style and optimally organised, it will prove useful for the advanced graduate as well as for the experienced researcher.

Functional analysis. --- Calculus. --- Operator theory. --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Operator Theory. --- Functional Analysis.