Matches in SemOpenAlex for { <https://semopenalex.org/work/W2018299957> ?p ?o ?g. }
Showing items 1 to 52 of
52
with 100 items per page.
- W2018299957 abstract "For an arbitrary open set {omega} subset of I{sup 2}=[0,1){sup 2} and an arbitrary function f element of L log {sup +}L log {sup +} log {sup +}L(I{sup 2}) such that f=0 on {omega} the double Fourier series of f with respect to the trigonometric system {psi}=E and the Walsh-Paley system {psi}=W is shown to converge to zero (over rectangles) almost everywhere on {omega}. Thus, it is proved that generalized localization almost everywhere holds on arbitrary open subsets of the square I{sup 2} for the double trigonometric Fourier series and the Walsh-Fourier series of functions in the class L log {sup +}L log {sup +} log {sup +}L (in the case of summation over rectangles). It is also established that such localization breaks down on arbitrary sets that are not dense in I{sup 2}, in the classes {phi}{sub {psi}}(L)(I{sup 2}) for the orthonormal system {psi}=E and an arbitrary function such that {phi}{sub E}(u)=o(u log {sup +} log {sup +}u) as u{yields}{infinity} or for {phi}{sub W}(u)=u( log {sup +} log {sup +}u){sup 1-{epsilon}}, 0<{epsilon}<1." @default.
- W2018299957 created "2016-06-24" @default.
- W2018299957 creator A5031272525 @default.
- W2018299957 creator A5071855639 @default.
- W2018299957 creator A5080084490 @default.
- W2018299957 date "1998-06-30" @default.
- W2018299957 modified "2023-09-26" @default.
- W2018299957 title "Generalized localization for the double trigonometric Fourier series and the Walsh-Fourier series of functions in L log {sup +}L log {sup +} log {sup +}L" @default.
- W2018299957 doi "https://doi.org/10.1070/sm1998v189n05abeh000318;" @default.
- W2018299957 hasPublicationYear "1998" @default.
- W2018299957 type Work @default.
- W2018299957 sameAs 2018299957 @default.
- W2018299957 citedByCount "0" @default.
- W2018299957 crossrefType "journal-article" @default.
- W2018299957 hasAuthorship W2018299957A5031272525 @default.
- W2018299957 hasAuthorship W2018299957A5071855639 @default.
- W2018299957 hasAuthorship W2018299957A5080084490 @default.
- W2018299957 hasConcept C114614502 @default.
- W2018299957 hasConcept C121332964 @default.
- W2018299957 hasConcept C134306372 @default.
- W2018299957 hasConcept C14036430 @default.
- W2018299957 hasConcept C143724316 @default.
- W2018299957 hasConcept C151730666 @default.
- W2018299957 hasConcept C207864730 @default.
- W2018299957 hasConcept C27142425 @default.
- W2018299957 hasConcept C2779557605 @default.
- W2018299957 hasConcept C33923547 @default.
- W2018299957 hasConcept C62520636 @default.
- W2018299957 hasConcept C78458016 @default.
- W2018299957 hasConcept C86803240 @default.
- W2018299957 hasConceptScore W2018299957C114614502 @default.
- W2018299957 hasConceptScore W2018299957C121332964 @default.
- W2018299957 hasConceptScore W2018299957C134306372 @default.
- W2018299957 hasConceptScore W2018299957C14036430 @default.
- W2018299957 hasConceptScore W2018299957C143724316 @default.
- W2018299957 hasConceptScore W2018299957C151730666 @default.
- W2018299957 hasConceptScore W2018299957C207864730 @default.
- W2018299957 hasConceptScore W2018299957C27142425 @default.
- W2018299957 hasConceptScore W2018299957C2779557605 @default.
- W2018299957 hasConceptScore W2018299957C33923547 @default.
- W2018299957 hasConceptScore W2018299957C62520636 @default.
- W2018299957 hasConceptScore W2018299957C78458016 @default.
- W2018299957 hasConceptScore W2018299957C86803240 @default.
- W2018299957 hasIssue "5" @default.
- W2018299957 hasLocation W20182999571 @default.
- W2018299957 hasOpenAccess W2018299957 @default.
- W2018299957 hasPrimaryLocation W20182999571 @default.
- W2018299957 hasVolume "189" @default.
- W2018299957 isParatext "false" @default.
- W2018299957 isRetracted "false" @default.
- W2018299957 magId "2018299957" @default.
- W2018299957 workType "article" @default.