Fourier Analysis: Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations

✍ Scribed by Neal Bez, Mitsuru Sugimoto (auth.), Michael Ruzhansky, Ville Turunen (eds.)

Publisher: Birkhäuser Basel
Year: 2014
Tongue: English
Leaves: 416
Series: Trends in Mathematics
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. It is based on lectures given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland. This collection of 20 refereed articles is based on selected talks and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”

✦ Table of Contents

Front Matter....Pages i-viii
Optimal Constant for a Smoothing Estimate of Critical Index....Pages 1-7
The Interplay Between Time-dependent Speed of Propagation and Dissipation in Wave Models....Pages 9-45
A Note on Complete Hyperbolic Operators with log-Zygmund Coefficients....Pages 47-72
A Few Remarks on Time-frequency Analysis of Gevrey, Analytic and Ultra-analytic Functions....Pages 73-90
Global Wave-front Sets of Intersection and Union Type....Pages 91-106
A Pseudo-differential Calculus on Graded Nilpotent Lie Groups....Pages 107-132
L p Microlocal Properties for Vector Weighted Pseudodifferential Operators with Smooth Symbols....Pages 133-148
A Parametrix Construction for the Laplacian on ℚ-rank 1 Locally Symmetric Spaces....Pages 149-186
A Class of Elliptic Operators on a Manifold with Edge and Boundary....Pages 187-209
A Representation of the Fundamental Solution for the Fokker–Planck Equation and Its Application....Pages 211-233
The Fourier Transform and Convolutions Generated by a Differential Operator with Boundary Condition on a Segment....Pages 235-251
Global Existence for Quadratically Perturbed Massless Dirac Equations Under the Null Condition....Pages 253-262
Singular Partial Differential Operators and Pseudo-differential Boundary Conditions in Invisibility Cloaking....Pages 263-284
Perturbed Besov Spaces by a Short-range Type Potential in an Exterior Domain....Pages 285-309
On the Cauchy Problem for Hyperbolic Operators with Double Characteristics, a Transition Case....Pages 311-334
Differentiation Functor and Its Application in the Optimization Control Theory....Pages 335-347
The Solution of the Initial Mixed Boundary Value Problem for Hyperbolic Equations by Monte Carlo and Probability Difference Methods....Pages 349-355
Weak Monotonicity Concept and Its Applications....Pages 357-374
Critical Exponent for the Semilinear Wave Equation with Scale Invariant Damping....Pages 375-390
Semilinear Hyperbolic Equations in Curved Spacetime....Pages 391-415

✦ Subjects

Partial Differential Equations; Global Analysis and Analysis on Manifolds; Operator Theory; Abstract Harmonic Analysis; Sequences, Series, Summability; Real Functions

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