Geodesic Beams in Eigenfunction Analysis

This book discusses the modern theory of Laplace eigenfunctions through the lens of a new tool called geodesic beams. The authors provide a brief introduction to the theory of Laplace eigenfunctions followed by an accessible treatment of geodesic beams and their applications to sup norm estimates, L^p estimates,  averages, and Weyl laws.  Geodesic beams have proven to be a valuable tool in the study of Laplace eigenfunctions, but their treatment is currently spread through a variety of rather technical papers. The authors present a treatment of these tools that is accessible to a wider audience of mathematicians. Readers will gain an introduction to geodesic beams and the modern theory of Laplace eigenfunctions, which will enable them to understand the cutting edge aspects of this theory.

List of contents

Introduction.- The Laplace operator.- Axiomatic introduction to semiclassical analysis.- Basic properties of eigenfunctions and eigenvalues.- The Koch-Tataru-Zworski approach to L estimates.- Geodesic Beam Tools.- Applications of the geodesic beam decomposition.- Dynamical ideas.

Report

"The book is adequate for advanced graduate students familiarized with semiclassical analysis. It might be an excellent choice for a reading course." (Emilio A. Lauret, zbMATH 1545.58001, 2024)

Product details

• Authors: Yaiza Canzani, Jeffrey Galkowski
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 15.06.2024
• EAN: 9783031315886
• ISBN: 978-3-0-3131588-6
• No. of pages: 116
• Dimensions: 168 mm x 7 mm x 240 mm
• Weight: 229 g
• Illustrations: X, 116 p. 19 illus., 6 illus. in color.
• Series: Synthesis Lectures on Mathematics & Statistics
• Subject: Natural sciences, medicine, IT, technology > Physics, astronomy > Theoretical physics