Microlocal energy methods and pseudo-differential operators
type: Item
instance of: scholarly article
title: Microlocal energy methods and pseudo-differential operators
zbMATH Open document ID: 0552.58031
DOI: 10.1007/BF01389055
published in: Inventiones Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143257
review text: It is well known that analyticity and positivity for Hermite kernels are deeply connected. For example, the Hermite positivity is preserved under analytic continuations. In this paper, we combine these facts with the theory of microfunctions and pseudodifferential operators. We give methods of estimation of microanalyticity via Hermite positive microkernels. Moreover, in those methods, the positivity can be weakened to the so-called quasipositivity; this is formulated by employing a class of Hermite positive pseudodifferential operators with infinite order. These methods are very much like energy methods, and so we believe that they have many applications to problems of pseudo-differential equations.
Mathematics Subject Classification ID: 58J40
zbMATH DE Number: 3879779
zbMATH Keywords: Hermite kernels
zbMATH Keywords: microfunctions
zbMATH Keywords: pseudodifferential operators
zbMATH Keywords: microanalyticity
zbMATH Keywords: positive microkernels
zbMATH Keywords: quasipositivity
zbMATH Keywords: energy methods
author: Kiyoomi Kataoka
MaRDI profile type: Publication
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OpenAlex ID: W2034348686
description: scientific article; zbMATH DE number 3879779