Overview
- Provides a vast array of physical phenomena, ranging from the propagation of waves to the location of quantum particles
- Introduces the cutting edge theory and microlocal methods of geodesic beams
- Discusses how eigenfunctions of the Laplacian matrix play a crucial role both in physics and mathematics
Part of the book series: Synthesis Lectures on Mathematics & Statistics (SLMS)
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About this book
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.
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Keywords
Table of contents (8 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
About the authors
Yaiza Canzani, Ph.D., is Associate Professor in the Department of Mathematics at the University of North Carolina at Chapel Hill. She received her Ph.D. in Mathematics at McGill University. After graduating, Dr. Canzani held postdoctoral positions at Harvard University and the Institute for Advanced Study. Her work has been recognized with a Sloan Fellowship, an NSF CAREER grant, and the AWM Sadosky Prize in Analysis.
Jeffrey Galkowski, Ph.D., is Professor in the Department of Mathematics at University College London. He received his Ph.D. in Mathematics at University of California at Berkeley. Dr. Galkowski held a NSF Postdoctoral Fellowship at Stanford University and the CRM-ISM postdoctoral fellowship at McGill University. His work has been recognized with an EPSRC early career fellowship as well as the Adams Prize in Mathematics from the University of Cambridge.
Bibliographic Information
Book Title: Geodesic Beams in Eigenfunction Analysis
Authors: Yaiza Canzani, Jeffrey Galkowski
Series Title: Synthesis Lectures on Mathematics & Statistics
DOI: https://doi.org/10.1007/978-3-031-31586-2
Publisher: Springer Cham
eBook Packages: Synthesis Collection of Technology (R0), eBColl Synthesis Collection 12
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-31585-5Published: 14 June 2023
Softcover ISBN: 978-3-031-31588-6Published: 15 June 2024
eBook ISBN: 978-3-031-31586-2Published: 13 June 2023
Series ISSN: 1938-1743
Series E-ISSN: 1938-1751
Edition Number: 1
Number of Pages: X, 116
Number of Illustrations: 13 b/w illustrations, 6 illustrations in colour
Topics: Mathematical Methods in Physics, Quantum Physics, Particle and Nuclear Physics, Mathematical Physics, Mathematics, general