Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations: A Volume of Advances in Partial Differential Equations

✍ Scribed by P. R. Popivanov (auth.), Sergio Albeverio, Michael Demuth, Elmar Schrohe, Bert-Wolfgang Schulze (eds.)

Publisher: Birkhäuser Basel
Year: 2003
Tongue: English
Leaves: 440
Series: Operator Theory: Advances and Applications 145
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This volume focuses on recent developments in non-linear and hyperbolic equations.
In the first contribution, the singularities of the solutions of several classes of non-linear partial differential equations are investigated. Applications concern the Monge-Ampère equation, quasi-linear systems arising in fluid mechanics as well as integro-differential equations for media with memory.
There follows an article on L_p-L_q decay estimates for Klein-Gordon equations with time-dependent coefficients, explaining, in particular, the influence of the relation between the mass term and the wave propagation speed. The next paper addresses questions of local existence of solutions, blow-up criteria, and C^8 regularity for quasilinear weakly hyperbolic equations. Spectral theory of semibounded selfadjoint operators is the topic of a further contribution, providing upper and lower bounds for the bottom eigenvalue as well as an upper bound for the second eigenvalue in terms of capacitary estimates.

✦ Table of Contents

Front Matter....Pages i-v
Nonlinear PDE. Singularities, Propagation, Applications....Pages 1-94
From Wave to Klein—Gordon Type Decay Rates....Pages 95-155
Local Solutions to Quasi-linear Weakly Hyperbolic Differential Equations....Pages 157-205
An Approach to a Version of the S(M , g)- pseudo-differential Calculus on Manifolds....Pages 207-248
Spectral Invariance and Submultiplicativity for the Algebras of S ( M , g )-pseudo-differential Operators on Manifolds....Pages 249-280
Domain Perturbations and Capacity in General Hilbert Spaces and Applications to Spectral Theory....Pages 281-362
An Interpolation Family between Gabor and Wavelet Transformations....Pages 363-394
Formes de torsion analytique et fibrations singulières....Pages 395-418
Regularisation of Secondary Characteristic Classes and Unusual Index Formulas for Operator-valued Symbols....Pages 419-437

✦ Subjects

Operator Theory;Functional Analysis;Partial Differential Equations;Mathematical Methods in Physics

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