Matches in SemOpenAlex for { <https://semopenalex.org/work/W2077844891> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W2077844891 abstract "Let Y be a locally compact group, Aut(Y) be the group of topological automorphisms of Y and ℙ(Y) be the set of continuous positive definite functions on Y which have unit value at the identity. A function Φ ∈ ℙ (Y 2 ) is said to be of product type if there are such functions Φ j ∈ ℙ (Y) that Φ(u, v) = Φ 1 (u)Φ 2 (v). Define the mapping T: Y 2 → Y 2 by the formula T(u, v) = (A 1 uA 2 v, A 3 u A 4 v), where A j ∈ Aut(Y), and assume that T is a one-to-one transform. K. Schmidt proved: (i) if both Φ(u, v) and Φ(T(u, v)) are of product type, then the functions Φ j are infinitely divisible; (ii) if Y is Abelian, both Φ(u, v) and Φ(T(u, v)) are of product type, and Φ(u, v) ≠ 0, then the functions Φ j are Gaussian. We show that statement (i), generally, is not valid, but K. Schmidt's proof holds true if Φ(u, v) ≠ 0. We also give another proof of statement (ii). Our proof uses neither the Levy-Khinchin formula for a continuous infinitely divisible positive definite function nor (i) on which K. Schmidt's proof is based." @default.
- W2077844891 created "2016-06-24" @default.
- W2077844891 creator A5020668017 @default.
- W2077844891 date "2009-01-24" @default.
- W2077844891 modified "2023-09-26" @default.
- W2077844891 title "On a theorem of K. Schmidt" @default.
- W2077844891 doi "https://doi.org/10.1112/blms/bdn111" @default.
- W2077844891 hasPublicationYear "2009" @default.
- W2077844891 type Work @default.
- W2077844891 sameAs 2077844891 @default.
- W2077844891 citedByCount "4" @default.
- W2077844891 countsByYear W20778448912012 @default.
- W2077844891 countsByYear W20778448912013 @default.
- W2077844891 countsByYear W20778448912019 @default.
- W2077844891 crossrefType "journal-article" @default.
- W2077844891 hasAuthorship W2077844891A5020668017 @default.
- W2077844891 hasConcept C114614502 @default.
- W2077844891 hasConcept C118615104 @default.
- W2077844891 hasConcept C118712358 @default.
- W2077844891 hasConcept C18903297 @default.
- W2077844891 hasConcept C2524010 @default.
- W2077844891 hasConcept C2777299769 @default.
- W2077844891 hasConcept C33923547 @default.
- W2077844891 hasConcept C86803240 @default.
- W2077844891 hasConcept C90673727 @default.
- W2077844891 hasConceptScore W2077844891C114614502 @default.
- W2077844891 hasConceptScore W2077844891C118615104 @default.
- W2077844891 hasConceptScore W2077844891C118712358 @default.
- W2077844891 hasConceptScore W2077844891C18903297 @default.
- W2077844891 hasConceptScore W2077844891C2524010 @default.
- W2077844891 hasConceptScore W2077844891C2777299769 @default.
- W2077844891 hasConceptScore W2077844891C33923547 @default.
- W2077844891 hasConceptScore W2077844891C86803240 @default.
- W2077844891 hasConceptScore W2077844891C90673727 @default.
- W2077844891 hasLocation W20778448911 @default.
- W2077844891 hasOpenAccess W2077844891 @default.
- W2077844891 hasPrimaryLocation W20778448911 @default.
- W2077844891 hasRelatedWork W1798491552 @default.
- W2077844891 hasRelatedWork W2003121586 @default.
- W2077844891 hasRelatedWork W2016749366 @default.
- W2077844891 hasRelatedWork W2031078996 @default.
- W2077844891 hasRelatedWork W2050456612 @default.
- W2077844891 hasRelatedWork W2057422864 @default.
- W2077844891 hasRelatedWork W2073585441 @default.
- W2077844891 hasRelatedWork W2073773175 @default.
- W2077844891 hasRelatedWork W2095436529 @default.
- W2077844891 hasRelatedWork W21523136 @default.
- W2077844891 hasRelatedWork W2166844249 @default.
- W2077844891 hasRelatedWork W2226760130 @default.
- W2077844891 hasRelatedWork W2245722260 @default.
- W2077844891 hasRelatedWork W2740951103 @default.
- W2077844891 hasRelatedWork W2792875405 @default.
- W2077844891 hasRelatedWork W2950846454 @default.
- W2077844891 hasRelatedWork W2952367927 @default.
- W2077844891 hasRelatedWork W3102473047 @default.
- W2077844891 hasRelatedWork W3145170355 @default.
- W2077844891 hasRelatedWork W2186537027 @default.
- W2077844891 isParatext "false" @default.
- W2077844891 isRetracted "false" @default.
- W2077844891 magId "2077844891" @default.
- W2077844891 workType "article" @default.