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- W3087766803 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 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 estimates à la Stein-Tomas. This allows us to obtain sharp spectral multiplier theorems and hence sharp Bochner-Riesz summability results in some situation. Finally, we consider the random walk on the integer lattice Zn and prove sharp Bochner-Riesz summability results similar to those known for the standard Laplacian on Rn. Nous présentons, dans un cadre abstrait, des théorèmes de multiplicateurs spectraux pour des opérateurs auto-adjoints sur des espaces de type homogène. Nous poursuivons deux objectifs principaux. Le premier est de ne pas faire appel au semi-groupe et de pouvoir ainsi se passer de certaines hypothèses habituelles sur celui-ci. Le second est de considérer des décroissances hors-diagonales polynômiales au lieu d'exponentielles. Nos résultats s'appliquent à divers opérateurs tels que des opérateurs différentiels, pseudo-différentiels ou des chaines de Markov. Nous introduisons également des estimations de restriction de type Stein-Tomas. Celles-ci sont ensuite utilisées pour obtenir des résultats optimaux sur les moyennes de Bochner-Riesz. Finalement, nous considérons la marche aléatoire sur Zn et nous montrons des résultats optimaux sur les moyennes de Bochner-Riesz correspondantes. Ces résultats sont similaires à ceux connus pour le laplacien sur Rn." @default.
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- W3087766803 date "2020-11-01" @default.
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- W3087766803 title "Spectral multipliers without semigroup framework and application to random walks" @default.
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- W3087766803 doi "https://doi.org/10.1016/j.matpur.2020.09.009" @default.
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