Harmonic Analysis and Applications
About this Title
Carlos E. Kenig, University of Chicago, Chicago, IL, Fang Hua Lin, New York University, Courant Institute, New York, NY, Svitlana Mayboroda, University of Minnesota, Minneapolis, MN and Tatiana Toro, University of Washington, Seattle, WA, Editors
Publication: IAS/Park City Mathematics Series
Publication Year: 2020; Volume 27
ISBNs: 978-1-4704-6127-0 (print); 978-1-4704-6281-9 (online)
The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics.
The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.
Graduate students and researchers interested in harmonic analysis and its applications to diffusion processes and propagation of waves.
Table of Contents
- Alexander Logunov and Eugenia Malinnikova – Lecture notes on quantitative unique continuation for solutions of second order elliptic equations
- Svetlana Jitomirskaya, Wencai Liu and Shiwen Zhang – Arithmetic spectral transitions: A competition between hyperbolicity and the arithmetics of small denominators
- Zhongwei Shen – Quantitative homogenization of elliptic operators with periodic coefficients
- Charles Smart – Stochastic homogenization of elliptic equations
- Simon Bortz, Steve Hofmann and José Luna – T1 and Tb theorems and applications
- Guy David – Sliding almost minimal sets and the Plateau problem
- Camillo De Lellis – Almgren’s center manifold in a simple setting
- Aaron Naber – Lecture notes on rectifiable Reifenberg for measures