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Nicola, Fabio.
Global Pseudo-Differential Calculus on Euclidean Spaces [electronic resource] / by Fabio Nicola, Luigi Rodino. - X, 306 p. online resource. - Pseudo-Differential Operators, Theory and Applications ; 4 .
Background meterial -- Global Pseudo-Differential Calculus -- ?-Pseudo-Differential Operators and H-Polynomials -- G-Pseudo-Differential Operators -- Spectral Theory -- Non-Commutative Residue and Dixmier Trace -- Exponential Decay and Holomorphic Extension of Solutions.
This book is devoted to the global pseudo-differential calculus on Euclidean spaces and its applications to geometry and mathematical physics, with emphasis on operators of linear and non-linear quantum physics and travelling waves equations. The pseudo-differential calculus presented here has an elementary character, being addressed to a large audience of scientists. It includes the standard classes with global homogeneous structures, the so-called G and gamma operators. Concerning results for the applications, a first main line is represented by spectral theory. Beside complex powers of operators and asymptotics for the counting function, particular attention is here devoted to the non-commutative residue in Euclidean spaces and the Dixmier trace. Second main line is the self-contained presentation, for the first time in a text-book form, of the problem of the holomorphic extension of the solutions of the semi-linear globally elliptic equations. Entire extensions are discussed in detail. Exponential decay is simultaneously studied.
9783764385125
Mathematics.
Fourier analysis.
Functional analysis.
Global analysis.
Differential equations, partial.
Mathematics.
Partial Differential Equations.
Global Analysis and Analysis on Manifolds.
Fourier Analysis.
Functional Analysis.
QA370-380
515.353
Global Pseudo-Differential Calculus on Euclidean Spaces [electronic resource] / by Fabio Nicola, Luigi Rodino. - X, 306 p. online resource. - Pseudo-Differential Operators, Theory and Applications ; 4 .
Background meterial -- Global Pseudo-Differential Calculus -- ?-Pseudo-Differential Operators and H-Polynomials -- G-Pseudo-Differential Operators -- Spectral Theory -- Non-Commutative Residue and Dixmier Trace -- Exponential Decay and Holomorphic Extension of Solutions.
This book is devoted to the global pseudo-differential calculus on Euclidean spaces and its applications to geometry and mathematical physics, with emphasis on operators of linear and non-linear quantum physics and travelling waves equations. The pseudo-differential calculus presented here has an elementary character, being addressed to a large audience of scientists. It includes the standard classes with global homogeneous structures, the so-called G and gamma operators. Concerning results for the applications, a first main line is represented by spectral theory. Beside complex powers of operators and asymptotics for the counting function, particular attention is here devoted to the non-commutative residue in Euclidean spaces and the Dixmier trace. Second main line is the self-contained presentation, for the first time in a text-book form, of the problem of the holomorphic extension of the solutions of the semi-linear globally elliptic equations. Entire extensions are discussed in detail. Exponential decay is simultaneously studied.
9783764385125
Mathematics.
Fourier analysis.
Functional analysis.
Global analysis.
Differential equations, partial.
Mathematics.
Partial Differential Equations.
Global Analysis and Analysis on Manifolds.
Fourier Analysis.
Functional Analysis.
QA370-380
515.353