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9783764321680

Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations

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  • ISBN13:

    9783764321680

  • ISBN10:

    3764321687

  • Format: Hardcover
  • Copyright: 2004-01-01
  • Publisher: Birkhauser

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Summary

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

Preface
Nonlinear PDE. Singularities, Propagation, Applicationsp. 1
From Wave to Klein-Gordon Type Decay Ratesp. 95
Local Solutions to Quasi-linear Weakly Hyperbolic Differential Equationsp. 157
An Approach to a Version of the S(M, g)-pseudo-differential Calculus on Manifoldsp. 207
Spectral Invariance and Submultiplicativity for the Algebras of S(M, g)-pseudo-differential Operators on Manifoldsp. 249
Domain Perturbations and Capacity in General Hilbert Spaces and Applications to Spectral Theoryp. 281
An Interpolation Family between Gabor and Wavelet Transformations. Application to Differential Calculus and Construction of Anisotropic Banach Spacesp. 363
Formes de torsion analytique et fibrations singulieresp. 395
Regularisation of Secondary Characteristic Classes and Unusual Index Formulas for Operator-valued Symbolsp. 419
Table of Contents provided by Blackwell. All Rights Reserved.

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