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Geodesic Beams in Eigenfunction Analysis: Synthesis Lectures on Mathematics & Statistics

Autor Yaiza Canzani, Jeffrey Galkowski
en Limba Engleză Paperback – 15 iun 2024
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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Specificații

ISBN-13: 9783031315886
ISBN-10: 303131588X
Pagini: 116
Ilustrații: X, 116 p. 19 illus., 6 illus. in color.
Dimensiuni: 168 x 240 x 10 mm
Greutate: 0.24 kg
Ediția:2023
Editura: Springer International Publishing
Colecția Springer
Seria Synthesis Lectures on Mathematics & Statistics

Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică

Yaiza CanzaniPh.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 GalkowskiPh.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.

Textul de pe ultima copertă

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.
This book:
  • Reviews several physical phenomena related to Laplace eigenfunctions, 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 play a crucial role both in physics and mathematics.

Caracteristici

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