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Transmutation Theory and Applications

Differential operators. --- Transmutation operators. --- Operators, Transmutation --- Operator theory --- Operators, Differential --- Differential equations

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The main aim of this book is to introduce the reader to the concept of comparison algebra, defined as a type of C*-algebra of singular integral operators. The first part of the book develops the necessary elements of the spectral theory of differential operators as well as the basic properties of elliptic second order differential operators. The author then introduces comparison algebras and describes their theory in L2-spaces and L2-Soboler spaces, and in particular their importance in solving functional analytic problems involving differential operators. The book is based on lectures given in Sweden and the USA.

Differential operators. --- Linear operators. --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Operators, Differential --- Differential equations

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The theory of Lebesgue and Sobolev spaces with variable integrability is experiencing a steady expansion, and is the subject of much vigorous research by functional analysts, function-space analysts and specialists in nonlinear analysis. These spaces have attracted attention not only because of their intrinsic mathematical importance as natural, interesting examples of non-rearrangement-invariant function spaces but also in view of their applications, which include the mathematical modeling of electrorheological fluids and image restoration. The main focus of this book is to provide a solid fu

Function spaces. --- Sobolev spaces. --- Differential operators. --- Spaces, Sobolev --- Function spaces --- Operators, Differential --- Differential equations --- Operator theory --- Spaces, Function --- Functional analysis

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This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature.

Differential operators. --- Microlocal analysis. --- Functional analysis --- Operators, Differential --- Differential equations --- Operator theory --- Pseudodifferential operators --- Opérateurs pseudo-différentiels --- Singularities (Mathematics) --- Singularités (mathématiques) --- Analyse microlocale --- Fourier, Opérateurs intégraux de

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Periodic differential operators have a rich mathematical theory as well as important physical applications. They have been the subject of intensive development for over a century and remain a fertile research area. This book lays out the theoretical foundations and then moves on to give a coherent account of more recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations. The book will be valuable to advanced students and academics both for general reference and as an introduction to active research topics.

Mathematics. --- Operator algebras. --- Singularities (Mathematics). --- Differential operators --- Differential equations --- Operator theory --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Differential operators. --- Operators, Differential --- Operator theory. --- Differential equations. --- Ordinary Differential Equations. --- Operator Theory. --- 517.91 Differential equations --- Functional analysis --- Math --- Science --- Differential Equations.