Heat Kernels, Smoothness Estimates, and Exponential Decay

Albert Boggess, Andrew Raich

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 ℂn+1. On the transform side, the problem becomes establishing QSE on a heat kernel associated to the weighted ∂̄-operator on L2(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.

Original languageEnglish (US)
Pages (from-to)180-224
Number of pages45
JournalJournal of Fourier Analysis and Applications
Volume19
Issue number1
DOIs
StatePublished - 2013

Fingerprint

Heat Kernel
Exponential Decay
Smoothness
Polynomial Model
Estimate
Decay
Fourier transforms
Fourier transform
Transform
Hot Temperature
Operator
Statistical Models

Keywords

  • Decoupled polynomial model
  • Gaussian decay
  • Heat kernel
  • Polynomial model
  • Quantitative smoothness estimates
  • Szegö kernel
  • Weighted ∂̄-operator

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Analysis

Cite this

Heat Kernels, Smoothness Estimates, and Exponential Decay. / Boggess, Albert; Raich, Andrew.

In: Journal of Fourier Analysis and Applications, Vol. 19, No. 1, 2013, p. 180-224.

Research output: Contribution to journalArticle

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