Lectures on Hermite and Laguerre Expansions

The interplay between analysis on Lie groups and the theory of special functions is well known. This monograph deals with the case of the Heisenberg group and the related expansions in terms of Hermite, special Hermite, and Laguerre functions. The main thrust of the book is to develop a concrete Littlewood-Paley-Stein theory for these expansions and use the theory to prove multiplier theorems. The questions of almost-everywhere and mean convergence of Bochner-Riesz means are also treated. Most of the results in this monograph appear for the first time in book form.

About the author

Sundaram Thangavelu is a member of the Tata Institute of Fundamental Research in Bangalore, India.

Summary

The interplay between analysis on Lie groups and the theory of special functions is well known. This monograph deals with the case of the Heisenberg group and the related expansions in terms of Hermite, special Hermite, and Laguerre functions. The main thrust of the book is to develop a concrete Littlewood-Paley-Stein theory for these expansions and use the theory to prove multiplier theorems. The questions of almost-everywhere and mean convergence of Bochner-Riesz means are also treated. Most of the results in this monograph appear for the first time in book form.

Product details

• Authors: Sundaram Thangavelu, Thangavelu Sundaram
• Publisher: Princeton University Press
• Languages: English
• Product format: Paperback / Softback
• Released: 09.05.1993
• EAN: 9780691000480
• ISBN: 978-0-691-00048-0
• No. of pages: 214
• Series: Mathematical Notes; Mathematical Notes
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; MATHEMATICS / Group Theory, Groups & group theory, Groups and group theory