Matches in SemOpenAlex for { <https://semopenalex.org/work/W3200663793> ?p ?o ?g. }
- W3200663793 endingPage "1815" @default.
- W3200663793 startingPage "1801" @default.
- W3200663793 abstract "We are interested in the ‘smoothest’ averaging that can be achieved by convolving functions f ∈ ℓ 2 ( Z ) with an averaging function u. More precisely, suppose u : { − n , … , n } → R is a symmetric function normalized to ∑ k = − n n u ( k ) = 1 . We show that every convolution operator is not-too-smooth, in the sense that sup f ∈ ℓ 2 ( Z ) ∥ ∇ ( f ∗ u ) ∥ ℓ 2 ( Z ) ∥ f ∥ ℓ 2 ⩾ 2 2 n + 1 , and we show that equality holds if and only if u is constant on the interval { − n , … , n } . In the setting where smoothness is measured by the ℓ 2 -norm of the discrete second derivative and we further restrict our attention to functions u with nonnegative Fourier transform, we establish the inequality sup f ∈ ℓ 2 ( Z ) ∥ Δ ( f ∗ u ) ∥ ℓ 2 ( Z ) ∥ f ∥ ℓ 2 ( Z ) ⩾ 4 ( n + 1 ) 2 , with equality if and only if u is the triangle function u ( k ) = ( n + 1 − | k | ) / ( n + 1 ) 2 . We also discuss a continuous analogue and several open problems." @default.
- W3200663793 created "2021-09-27" @default.
- W3200663793 creator A5054778975 @default.
- W3200663793 creator A5064789268 @default.
- W3200663793 date "2021-09-15" @default.
- W3200663793 modified "2023-09-27" @default.
- W3200663793 title "The smoothest average: Dirichlet, Fejér and Chebyshev" @default.
- W3200663793 cites W1527702568 @default.
- W3200663793 cites W1533772917 @default.
- W3200663793 cites W1558981179 @default.
- W3200663793 cites W1970152983 @default.
- W3200663793 cites W1973976434 @default.
- W3200663793 cites W1975601543 @default.
- W3200663793 cites W1979311378 @default.
- W3200663793 cites W1991758894 @default.
- W3200663793 cites W2002312729 @default.
- W3200663793 cites W2003171351 @default.
- W3200663793 cites W2010548775 @default.
- W3200663793 cites W2015064056 @default.
- W3200663793 cites W2017990047 @default.
- W3200663793 cites W2020649744 @default.
- W3200663793 cites W2078908559 @default.
- W3200663793 cites W2094654291 @default.
- W3200663793 cites W2211048819 @default.
- W3200663793 cites W2320045903 @default.
- W3200663793 cites W2487898712 @default.
- W3200663793 cites W2962891031 @default.
- W3200663793 cites W2963573502 @default.
- W3200663793 cites W2963648422 @default.
- W3200663793 cites W2964095170 @default.
- W3200663793 cites W2964107813 @default.
- W3200663793 cites W2971085579 @default.
- W3200663793 cites W2995557624 @default.
- W3200663793 cites W3017008407 @default.
- W3200663793 cites W3022976132 @default.
- W3200663793 cites W3100291824 @default.
- W3200663793 cites W3138655353 @default.
- W3200663793 cites W4238768247 @default.
- W3200663793 cites W4242127901 @default.
- W3200663793 cites W4254215750 @default.
- W3200663793 cites W66366795 @default.
- W3200663793 doi "https://doi.org/10.1112/blms.12543" @default.
- W3200663793 hasPublicationYear "2021" @default.
- W3200663793 type Work @default.
- W3200663793 sameAs 3200663793 @default.
- W3200663793 citedByCount "0" @default.
- W3200663793 crossrefType "journal-article" @default.
- W3200663793 hasAuthorship W3200663793A5054778975 @default.
- W3200663793 hasAuthorship W3200663793A5064789268 @default.
- W3200663793 hasBestOaLocation W32006637932 @default.
- W3200663793 hasConcept C102634674 @default.
- W3200663793 hasConcept C114614502 @default.
- W3200663793 hasConcept C119857082 @default.
- W3200663793 hasConcept C134306372 @default.
- W3200663793 hasConcept C14036430 @default.
- W3200663793 hasConcept C17744445 @default.
- W3200663793 hasConcept C191795146 @default.
- W3200663793 hasConcept C199539241 @default.
- W3200663793 hasConcept C33923547 @default.
- W3200663793 hasConcept C41008148 @default.
- W3200663793 hasConcept C45347329 @default.
- W3200663793 hasConcept C50644808 @default.
- W3200663793 hasConcept C78458016 @default.
- W3200663793 hasConcept C86803240 @default.
- W3200663793 hasConceptScore W3200663793C102634674 @default.
- W3200663793 hasConceptScore W3200663793C114614502 @default.
- W3200663793 hasConceptScore W3200663793C119857082 @default.
- W3200663793 hasConceptScore W3200663793C134306372 @default.
- W3200663793 hasConceptScore W3200663793C14036430 @default.
- W3200663793 hasConceptScore W3200663793C17744445 @default.
- W3200663793 hasConceptScore W3200663793C191795146 @default.
- W3200663793 hasConceptScore W3200663793C199539241 @default.
- W3200663793 hasConceptScore W3200663793C33923547 @default.
- W3200663793 hasConceptScore W3200663793C41008148 @default.
- W3200663793 hasConceptScore W3200663793C45347329 @default.
- W3200663793 hasConceptScore W3200663793C50644808 @default.
- W3200663793 hasConceptScore W3200663793C78458016 @default.
- W3200663793 hasConceptScore W3200663793C86803240 @default.
- W3200663793 hasFunder F4320306076 @default.
- W3200663793 hasFunder F4320306151 @default.
- W3200663793 hasIssue "6" @default.
- W3200663793 hasLocation W32006637931 @default.
- W3200663793 hasLocation W32006637932 @default.
- W3200663793 hasOpenAccess W3200663793 @default.
- W3200663793 hasPrimaryLocation W32006637931 @default.
- W3200663793 hasRelatedWork W1173046508 @default.
- W3200663793 hasRelatedWork W1978042415 @default.
- W3200663793 hasRelatedWork W2017331178 @default.
- W3200663793 hasRelatedWork W2022749246 @default.
- W3200663793 hasRelatedWork W2041071417 @default.
- W3200663793 hasRelatedWork W2345668920 @default.
- W3200663793 hasRelatedWork W2592086716 @default.
- W3200663793 hasRelatedWork W2976797620 @default.
- W3200663793 hasRelatedWork W3086542228 @default.
- W3200663793 hasRelatedWork W4212986122 @default.
- W3200663793 hasVolume "53" @default.
- W3200663793 isParatext "false" @default.
- W3200663793 isRetracted "false" @default.