Titlebook: Evolution Equations of Hyperbolic and Schrödinger Type; Asymptotics, Estimat Michael Ruzhansky,Mitsuru Sugimoto,Jens Wirth Book 2012 Spring

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Divergence-type Operators: Spectral Theory and Spacetime Estimates,e (LAP) is proved in the framework of weighted Sobolev spaces. It is then used for (i) A general eigenfunction expansion theorem and (ii) Global spacetime estimates for the associated (inhomogeneous) generalized wave equation.

Decongestant

Modulus of Continuity and Decay at Infinity in Evolution Equations with Real Characteristics,where a sharp scale of Hölder continuity, with respect to the time variable ., for the a.’s has been established..We show that, for ., a lack of regularity in t can be compensated by a decay as the space variable x .This is not true in the hyperbolic case . = 1 because of the finite speed of propagation.

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Entrepreneurship and Historical Explanationnterplay between the wave equation on a Lorentzian manifold and corresponding Riemannian regularizations, and under additional regularity assumptions we derive bounds on the rate of convergence of their commutator. We also show that the restriction to underlying space-like foliations behaves well with respect to these regularizations.

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Book 2012dvances in the area in order to allow a quick overview of ongoing research. The contributors are first rate mathematicians. This collection of research papers is centred around parametrix constructions  and microlocal analysis; asymptotic constructions of solutions; energy and dispersive estimates;

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