NDLI: Heat Kernels, Smoothness Estimates, and Exponential Decay

Content Provider	Springer Nature Link
Author	Boggess, Albert Raich, Andrew
Copyright Year	2012
Abstract	In this article, we characterize functions whose Fourier transforms have exponential decay. We characterize such functions by showing that they satisfy a family of estimates that we call quantitative smoothness estimates (QSE). Using the QSE, we establish Gaussian decay in the “bad direction” for the □ b -heat kernel on polynomial models in ℂ n+1. On the transform side, the problem becomes establishing QSE on a heat kernel associated to the weighted $\bar{\partial}$ -operator on L 2(ℂ). The bounds are established with Duhamel’s formula and careful estimation. In ℂ2, we can prove both on and off-diagonal decay for the □ b -heat kernel on polynomial models.
Ending Page	224
Page Count	45
Starting Page	180
File Format	PDF
ISSN	10695869
e-ISSN	15315851
Journal	Journal of Fourier Analysis and Applications
Issue Number	1
Volume Number	19
Language	English
Publisher	SP Birkhäuser Verlag Boston
Publisher Date	2012-11-09
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Heat kernels in several complex variables Signal, Image and Speech Processing Heat kernel Szegö kernel Abstract Harmonic Analysis Mathematical Methods in Physics Polynomial model Quantitative smoothness estimates Fourier Analysis Decoupled polynomial model Approximations and Expansions $\overline\partial_b$ and $\overline\partial_b$ -Neumann operators Weighted $\bar{\partial}$ -operator Gaussian decay Partial Differential Equations Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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