Matches in SemOpenAlex for { <https://semopenalex.org/work/W2019565920> ?p ?o ?g. }
Showing items 1 to 63 of
63
with 100 items per page.
- W2019565920 endingPage "217" @default.
- W2019565920 startingPage "217" @default.
- W2019565920 abstract "In the first part of this paper, Lemmas (lol) and (1.4) provide a generalization of the fact that no Cauchy measures exist in the big disc. In the second part we show that this fact implies the existence of the H. Bohr and J. Favard counterexamples concerning harmonic and analytic almost periodic functions. Introduction. It is well known and easy to prove that in the big disc there are many Gleason parts out of the Silov boundary of the big disc algebra. Our aim in this note is to show how this fact implies (i) there are harmonic almost periodic functions in a half-plane such that their harmonic conjugates are not almost periodic in any strictly contained half-plane (see [6, Chapitre III, ?47]), and (ii) there are analytic almost periodic functions in a strip with no Laurent decomposition (see [5, p. 278]). 1. Gleason parts and uniform approximation. We say that A is a uniform algebra over the compact space X if (i) A C C(X) and it is closed in the uniform convergence topology, (ii) A separates the points of X and contains the constant functionsWe denote the spectrum of A by Sp (A). If x, y E Sp(A), l|x y|| will be the norm of x y as an element of the dual space of A. If x eSp(A) we write Ax =/E A: /(x) = 0, /being the Gelfand transform of /. If m 6 M(X) = lbounded measures on XI, m is the measure defined by m(/) = m(/T) (the conjugate measure). If x E Sp(A), Kx is the set of representing measures for x. If m 6 M(X) we write m 1 A when m is orthogonal to A. (1.1) Lemma. Let A be a uni/orm algebra over X and x, y ESp(A). The following are equivalent: (i) jlx yll = 2; (ii) 1 E Closure o/ (Ax + A)= Cl (Ax + Ay) (Ay = AyD). Proof. (ii)-*(i)Let /n E Ax and gn E Ay be such that n + gn conReceived by the editors March 8, 1973 and, in revised form, August 29, 1973. AMS (MOS) subject classifications (1970). Primary 46J10; Secondary 42A84. Copyright" @default.
- W2019565920 created "2016-06-24" @default.
- W2019565920 creator A5041053863 @default.
- W2019565920 date "1974-02-01" @default.
- W2019565920 modified "2023-09-27" @default.
- W2019565920 title "Gleason parts and certain counterexamples in the big disc context" @default.
- W2019565920 cites W1577634535 @default.
- W2019565920 cites W2001864976 @default.
- W2019565920 cites W2049025582 @default.
- W2019565920 cites W2057332321 @default.
- W2019565920 cites W2059550302 @default.
- W2019565920 cites W2102155004 @default.
- W2019565920 cites W2107869792 @default.
- W2019565920 cites W2321112535 @default.
- W2019565920 cites W3162117442 @default.
- W2019565920 cites W2288216809 @default.
- W2019565920 doi "https://doi.org/10.1090/s0002-9939-1974-0380421-0" @default.
- W2019565920 hasPublicationYear "1974" @default.
- W2019565920 type Work @default.
- W2019565920 sameAs 2019565920 @default.
- W2019565920 citedByCount "0" @default.
- W2019565920 crossrefType "journal-article" @default.
- W2019565920 hasAuthorship W2019565920A5041053863 @default.
- W2019565920 hasBestOaLocation W20195659201 @default.
- W2019565920 hasConcept C114614502 @default.
- W2019565920 hasConcept C134306372 @default.
- W2019565920 hasConcept C162838799 @default.
- W2019565920 hasConcept C17744445 @default.
- W2019565920 hasConcept C191795146 @default.
- W2019565920 hasConcept C199539241 @default.
- W2019565920 hasConcept C202444582 @default.
- W2019565920 hasConcept C33923547 @default.
- W2019565920 hasConcept C627467 @default.
- W2019565920 hasConceptScore W2019565920C114614502 @default.
- W2019565920 hasConceptScore W2019565920C134306372 @default.
- W2019565920 hasConceptScore W2019565920C162838799 @default.
- W2019565920 hasConceptScore W2019565920C17744445 @default.
- W2019565920 hasConceptScore W2019565920C191795146 @default.
- W2019565920 hasConceptScore W2019565920C199539241 @default.
- W2019565920 hasConceptScore W2019565920C202444582 @default.
- W2019565920 hasConceptScore W2019565920C33923547 @default.
- W2019565920 hasConceptScore W2019565920C627467 @default.
- W2019565920 hasIssue "2" @default.
- W2019565920 hasLocation W20195659201 @default.
- W2019565920 hasOpenAccess W2019565920 @default.
- W2019565920 hasPrimaryLocation W20195659201 @default.
- W2019565920 hasRelatedWork W1971408836 @default.
- W2019565920 hasRelatedWork W2028667918 @default.
- W2019565920 hasRelatedWork W2036898190 @default.
- W2019565920 hasRelatedWork W2158105450 @default.
- W2019565920 hasRelatedWork W2313285636 @default.
- W2019565920 hasRelatedWork W2316076766 @default.
- W2019565920 hasRelatedWork W2316511563 @default.
- W2019565920 hasRelatedWork W2907544013 @default.
- W2019565920 hasRelatedWork W2962690600 @default.
- W2019565920 hasRelatedWork W2164026635 @default.
- W2019565920 hasVolume "45" @default.
- W2019565920 isParatext "false" @default.
- W2019565920 isRetracted "false" @default.
- W2019565920 magId "2019565920" @default.
- W2019565920 workType "article" @default.