CHEN, Peng; OUHABAZ, El Maati; SIKORA, Adam; YAN, Lixin

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CHEN, Peng
Guangzhou University

OUHABAZ, El Maati
Institut de Mathématiques de Bordeaux [IMB]

SIKORA, Adam
Macquarie University

Langue

Document de travail - Pré-publication

Résumé en anglais

In this paper we prove spectral multiplier theorems for abstract self-adjoint operators on spaces of homogeneous type. We have two main objectives. The first one is to work outside the semigroup context. In contrast to previous works on this subject, we do not make any assumption on the semigroup. The second objective is to consider polynomial off-diagonal decay instead of exponential one. Our approach and results lead to new applications to several operators such as differential operators, pseudo-differential operators as well as Markov chains. In our general context we introduce a restriction type estimatesàestimates`estimatesà la Stein-Tomas. This allows us to obtain sharp spectral multiplier theorems and hence sharp Bochner-Riesz summability results. Finally, we consider the random walk on the integer lattice Z n and prove sharp Bochner-Riesz summability results similar to those known for the standard Laplacian on R n .< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192919

Project ANR

Analyse Réelle et Géométrie - ANR-18-CE40-0012

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251