Convolution kernels versus spectral multipliers for sub-Laplacians on groups of polynomial growth

Alessio Martini; Fulvio Ricci; Leonardo Tolomeo

doi:10.1016/j.jfa.2019.05.024

Convolution kernels versus spectral multipliers for sub-Laplacians on groups of polynomial growth

Alessio Martini, Fulvio Ricci, Leonardo Tolomeo

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

141 Downloads (Pure)

Abstract

Let L be a sub-Laplacian on a connected Lie group G of polynomial growth. It is well known that, if F:R→C is in the Schwartz class S(R), then the convolution kernel K _F(L) of the operator F(L) is in the Schwartz class S(G). Here we prove a sort of converse implication for a class of groups G including all solvable noncompact groups of polynomial growth. We also discuss the problem whether integrability of K _F(L) implies continuity of F.

Original language	English
Pages (from-to)	1603-1638
Number of pages	36
Journal	Journal of Functional Analysis
Volume	277
Issue number	6
Early online date	4 Jun 2019
DOIs	https://doi.org/10.1016/j.jfa.2019.05.024
Publication status	Published - 15 Sept 2019

Keywords

Lie group
Riemann–Lebesgue lemma
Schwartz class
Sub-Laplacian

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2019.05.024Licence: None: All rights reserved

Alessio_Martini_et_al_Convolution_kernels_versus_spectral_multipliers_Journal_of_Functional_Analysis_2019
Checked for eligibility: 30/05/2019
Accepted author manuscript, 537 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

Sub-Elliptic Harmonic Analysis
Martini, A. (Principal Investigator)
Engineering & Physical Science Research Council
1/01/17 → 31/12/18
Project: Research Councils

Cite this

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abstract = "Let L be a sub-Laplacian on a connected Lie group G of polynomial growth. It is well known that, if F:R→C is in the Schwartz class S(R), then the convolution kernel K F(L) of the operator F(L) is in the Schwartz class S(G). Here we prove a sort of converse implication for a class of groups G including all solvable noncompact groups of polynomial growth. We also discuss the problem whether integrability of K F(L) implies continuity of F. ",

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AU - Ricci, Fulvio

AU - Tolomeo, Leonardo

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Y1 - 2019/9/15

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AB - Let L be a sub-Laplacian on a connected Lie group G of polynomial growth. It is well known that, if F:R→C is in the Schwartz class S(R), then the convolution kernel K F(L) of the operator F(L) is in the Schwartz class S(G). Here we prove a sort of converse implication for a class of groups G including all solvable noncompact groups of polynomial growth. We also discuss the problem whether integrability of K F(L) implies continuity of F.

KW - Lie group

KW - Riemann–Lebesgue lemma

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KW - Sub-Laplacian

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 6

ER -

Convolution kernels versus spectral multipliers for sub-Laplacians on groups of polynomial growth

Abstract

Keywords

ASJC Scopus subject areas

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Sub-Elliptic Harmonic Analysis

Cite this