SHARP SPECTRAL MULTIPLIERS WITHOUT SEMIGROUP FRAMEWORK AND APPLICATION TO RANDOM WALKS
Language
en
Document de travail - Pré-publication
English Abstract
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 ...Read more >
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 .Read less <
ANR Project
Analyse Réelle et Géométrie - ANR-18-CE40-0012
Origin
Hal imported