Matches in SemOpenAlex for { <https://semopenalex.org/work/W4290994101> ?p ?o ?g. }
Showing items 1 to 66 of
66
with 100 items per page.
- W4290994101 abstract "We investigate convolution semigroups of probability measures with continuous densities on locally compact abelian groups, which have a discrete subgroup such that the factor group is compact. Two interesting examples of the quotient structure are the $d$--dimensional torus, and the ad`{e}lic circle. Our main result is to show that the Poisson summation formula for the density can be interpreted as a probabilistic trace formula, linking values of the density on the factor group to the trace of the associated semigroup on $L^{2}$-space. The Gaussian is a very important example. For rotationally invariant $alpha$-stable densities, the trace formula is valid, but we cannot verify the Poisson summation formula. To prepare to study semistable laws on the ad`{e}les, we first investigate these on the $p$--adics, where we show they have continuous densities which may be represented as series expansions. We use these laws to construct a convolution semigroup on the ad`{e}les whose densities fail to satisfy the probabilistic trace formula." @default.
- W4290994101 created "2022-08-13" @default.
- W4290994101 creator A5051980041 @default.
- W4290994101 date "2016-02-03" @default.
- W4290994101 modified "2023-09-28" @default.
- W4290994101 title "Probabilistic Trace and Poisson Summation Formulae on Locally Compact Abelian Groups" @default.
- W4290994101 doi "https://doi.org/10.48550/arxiv.1602.01252" @default.
- W4290994101 hasPublicationYear "2016" @default.
- W4290994101 type Work @default.
- W4290994101 citedByCount "0" @default.
- W4290994101 crossrefType "posted-content" @default.
- W4290994101 hasAuthorship W4290994101A5051980041 @default.
- W4290994101 hasBestOaLocation W42909941011 @default.
- W4290994101 hasConcept C100906024 @default.
- W4290994101 hasConcept C102519508 @default.
- W4290994101 hasConcept C105795698 @default.
- W4290994101 hasConcept C119857082 @default.
- W4290994101 hasConcept C134306372 @default.
- W4290994101 hasConcept C136170076 @default.
- W4290994101 hasConcept C138885662 @default.
- W4290994101 hasConcept C202444582 @default.
- W4290994101 hasConcept C207405024 @default.
- W4290994101 hasConcept C31498916 @default.
- W4290994101 hasConcept C33923547 @default.
- W4290994101 hasConcept C41008148 @default.
- W4290994101 hasConcept C41895202 @default.
- W4290994101 hasConcept C45347329 @default.
- W4290994101 hasConcept C50644808 @default.
- W4290994101 hasConcept C64092710 @default.
- W4290994101 hasConcept C75291252 @default.
- W4290994101 hasConceptScore W4290994101C100906024 @default.
- W4290994101 hasConceptScore W4290994101C102519508 @default.
- W4290994101 hasConceptScore W4290994101C105795698 @default.
- W4290994101 hasConceptScore W4290994101C119857082 @default.
- W4290994101 hasConceptScore W4290994101C134306372 @default.
- W4290994101 hasConceptScore W4290994101C136170076 @default.
- W4290994101 hasConceptScore W4290994101C138885662 @default.
- W4290994101 hasConceptScore W4290994101C202444582 @default.
- W4290994101 hasConceptScore W4290994101C207405024 @default.
- W4290994101 hasConceptScore W4290994101C31498916 @default.
- W4290994101 hasConceptScore W4290994101C33923547 @default.
- W4290994101 hasConceptScore W4290994101C41008148 @default.
- W4290994101 hasConceptScore W4290994101C41895202 @default.
- W4290994101 hasConceptScore W4290994101C45347329 @default.
- W4290994101 hasConceptScore W4290994101C50644808 @default.
- W4290994101 hasConceptScore W4290994101C64092710 @default.
- W4290994101 hasConceptScore W4290994101C75291252 @default.
- W4290994101 hasLocation W42909941011 @default.
- W4290994101 hasLocation W42909941012 @default.
- W4290994101 hasLocation W42909941013 @default.
- W4290994101 hasLocation W42909941014 @default.
- W4290994101 hasOpenAccess W4290994101 @default.
- W4290994101 hasPrimaryLocation W42909941011 @default.
- W4290994101 hasRelatedWork W1970345540 @default.
- W4290994101 hasRelatedWork W1974535793 @default.
- W4290994101 hasRelatedWork W2057287380 @default.
- W4290994101 hasRelatedWork W2066904167 @default.
- W4290994101 hasRelatedWork W2114961260 @default.
- W4290994101 hasRelatedWork W2130721630 @default.
- W4290994101 hasRelatedWork W2625158582 @default.
- W4290994101 hasRelatedWork W2963698973 @default.
- W4290994101 hasRelatedWork W3101639582 @default.
- W4290994101 hasRelatedWork W4206662996 @default.
- W4290994101 isParatext "false" @default.
- W4290994101 isRetracted "false" @default.
- W4290994101 workType "article" @default.