Lectures on Hermite and Laguerre Expansions (eBook)

Sundaram Thangavelu (Autor)

eBook Download: PDF

2020
214 Seiten
Princeton University Press (Verlag)
978-0-691-21392-7 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 23.6.2020
• Reihe/Serie: Mathematical Notes
• Reihe/Serie: Mathematical Notes
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Schlagworte: Asymptote • Asymptotic Properties • Bessel function • Binomial coefficient • bounded function • boundedness • bounded operator • Class function (algebra) • Compact space • conjecture • Constants • convolution • corollary • counterexample • Critical Index • differential equation • Dimension • Eigenfunction • Eigenvalues and Eigenvectors • elliptic operator • estimation • Euclidean space • Finite difference • formula • Fourier series • Fourier transform • Function (mathematics) • Gegenbauer polynomials • Group representation • Haar measure • Harmonic Analysis • Heisenberg group • Hermite Polynomials • hypothesis • Integer • integers • Integration by parts • irreducible representation • Laguerre functions • Laguerre polynomials • Laplace's equation • Lebesgue measure • Lemma • Lie algebra • Lie group • Linear map • Lorentz Group • Lp space • Mathematical Physics • Mathematics • Mehler's formula • multiplication • Multipliers • Natural number • nilpotent group • Operator • orthonormal • Orthonormal basis • Oscillatory integral • oscillatory integrals • Plancherel theorem • Pointwise • Projection (linear algebra) • Proposition • Pure Mathematics • radial function • Radial Functions • Representation Theory • restriction theorem • Riesz • Riesz transform • Riesz Transforms • Semigroup • Singular integral • Smoothness • Special Functions • Special Hermite • Spectral Theorem • Spherical Harmonics • Summation • symmetric space • tensor product • Theorem • Transplantation • uniform boundedness • Upper and lower bounds • Variable (mathematics) • Vector field • wave equation • Young's inequality
• ISBN-10: 0-691-21392-5 / 0691213925
• ISBN-13: 978-0-691-21392-7 / 9780691213927