Advances in Harmonic Analysis and Partial Differential Equations

✍ Scribed by Vladimir Georgiev, Tohru Ozawa, Michael Ruzhansky, Jens Wirth

• Publisher: Springer International Publishing;Birkhäuser
• Year: 2020
• Tongue: English
• Leaves: 319
• Series: Trends in Mathematics
• Edition: 1st ed.
• Category: Library

✦ Synopsis

This book originates from the session "Harmonic Analysis and Partial Differential Equations" held at the 12th ISAAC Congress in Aveiro, andprovides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular non-linear PDEs. It can serve as a useful source of information to mathematicians, scientists and engineers.
The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.

✦ Table of Contents

Front Matter ....Pages i-x
Local Smoothing of Fourier Integral Operators and Hermite Functions (Ramesh Manna, P. K. Ratnakumar)....Pages 1-35
On (λ, μ)-Classes on the Engel Group (Marianna Chatzakou)....Pages 37-49
Gelfand Triples for the Kohn–Nirenberg Quantization on Homogeneous Lie Groups (Jonas Brinker, Jens Wirth)....Pages 51-97
A Multiplicity Result for a Non-Homogeneous Subelliptic Problem with Sobolev Exponent (Annunziata Loiudice)....Pages 99-120
The Dixmier Trace and the Noncommutative Residue for Multipliers on Compact Manifolds (Duván Cardona, César Del Corral)....Pages 121-163
On the Focusing Energy-Critical 3D Quintic Inhomogeneous NLS (Yonggeun Cho, Kiyeon Lee)....Pages 165-195
Lifespan of Solutions to Nonlinear Schrödinger Equations with General Homogeneous Nonlinearity of the Critical Order (Hayato Miyazaki, Motohiro Sobajima)....Pages 197-207
Spectral Theory for Magnetic Schrödinger Operators in Exterior Domains with Exploding and Oscillating Long-Range Potentials (Kiyoshi Mochizuki)....Pages 209-244
Simple Proof of the Estimate of Solutions to Schrödinger Equations with Linear and Sub-linear Potentials in Modulation Spaces (Keiichi Kato)....Pages 245-251
Remark on Asymptotic Order for the Energy Critical Nonlinear Damped Wave Equation to the Linear Heat Equation via the Strichartz Estimates (Takahisa Inui)....Pages 253-262
On Uniqueness for the Generalized Choquard Equation (Vladimir Georgiev, George Venkov)....Pages 263-278
Characterization of the Ground State to the Intercritical NLS with a Linear Potential by the Virial Functional (Masaru Hamano, Masahiro Ikeda)....Pages 279-307
Well-Posedness for a Generalized Klein-Gordon-Schrödinger Equations (Jishan Fan, Tohru Ozawa)....Pages 309-317

✦ Subjects

Mathematics; Analysis; Abstract Harmonic Analysis; Operator Theory