FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2615679942> ?p ?o ?g. }

• W2615679942 endingPage "94" @default.
• W2615679942 startingPage "87" @default.
• W2615679942 abstract "In this note we announce that under general hypotheses, wavelet-type expansions (of functions in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Superscript p> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{L^p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=1 less-than-or-equal-to p less-than-or-equal-to normal infinity> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>p</mml:mi> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>1 leq p leq infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, in one or more dimensions) converge pointwise almost everywhere, and identify the Lebesgue set of a function as a set of full measure on which they converge. It is shown that unlike the Fourier summation kernel, wavelet summation kernels <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper P Subscript j> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>j</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{P_j}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are bounded by radial decreasing <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Superscript 1> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{L^1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> convolution kernels. As a corollary it follows that best <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L squared> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{L^2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> spline approximations on uniform meshes converge pointwise almost everywhere. Moreover, summation of wavelet expansions is partially insensitive to order of summation. We also give necessary and sufficient conditions for given rates of convergence of wavelet expansions in the sup norm. Such expansions have order of convergence <italic>s</italic> if and only if the basic wavelet <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=psi> <mml:semantics> <mml:mi>ψ<!-- ψ --></mml:mi> <mml:annotation encoding=application/x-tex>psi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is in the homogeneous Sobolev space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H Subscript h Superscript negative s minus d slash 2> <mml:semantics> <mml:msubsup> <mml:mi>H</mml:mi> <mml:mi>h</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>−<!-- − --></mml:mo> <mml:mi>s</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mi>d</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:annotation encoding=application/x-tex>H_h^{ - s - d/2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We also present equivalent necessary and sufficient conditions on the scaling function. The above results hold in one and in multiple dimensions." @default.
• W2615679942 created "2017-05-26" @default.
• W2615679942 creator A5072017607 @default.
• W2615679942 date "1994-01-01" @default.
• W2615679942 modified "2023-10-01" @default.
• W2615679942 title "Pointwise convergence of wavelet expansions" @default.
• W2615679942 cites W1975474302 @default.
• W2615679942 cites W1986830331 @default.
• W2615679942 cites W1989582972 @default.
• W2615679942 cites W2013987111 @default.
• W2615679942 cites W2054777142 @default.
• W2615679942 cites W2096684483 @default.
• W2615679942 cites W2098914003 @default.
• W2615679942 cites W2615679942 @default.
• W2615679942 cites W4238865235 @default.
• W2615679942 cites W4255272544 @default.
• W2615679942 doi "https://doi.org/10.1090/s0273-0979-1994-00490-2" @default.
• W2615679942 hasPublicationYear "1994" @default.
• W2615679942 type Work @default.
• W2615679942 sameAs 2615679942 @default.
• W2615679942 citedByCount "70" @default.
• W2615679942 countsByYear W26156799422012 @default.
• W2615679942 countsByYear W26156799422013 @default.
• W2615679942 countsByYear W26156799422014 @default.
• W2615679942 countsByYear W26156799422016 @default.
• W2615679942 countsByYear W26156799422017 @default.
• W2615679942 countsByYear W26156799422018 @default.
• W2615679942 countsByYear W26156799422019 @default.
• W2615679942 countsByYear W26156799422021 @default.
• W2615679942 countsByYear W26156799422022 @default.
• W2615679942 countsByYear W26156799422023 @default.
• W2615679942 crossrefType "journal-article" @default.
• W2615679942 hasAuthorship W2615679942A5072017607 @default.
• W2615679942 hasBestOaLocation W26156799421 @default.
• W2615679942 hasConcept C11413529 @default.
• W2615679942 hasConcept C134306372 @default.
• W2615679942 hasConcept C154945302 @default.
• W2615679942 hasConcept C2777984123 @default.
• W2615679942 hasConcept C33923547 @default.
• W2615679942 hasConcept C41008148 @default.
• W2615679942 hasConceptScore W2615679942C11413529 @default.
• W2615679942 hasConceptScore W2615679942C134306372 @default.
• W2615679942 hasConceptScore W2615679942C154945302 @default.
• W2615679942 hasConceptScore W2615679942C2777984123 @default.
• W2615679942 hasConceptScore W2615679942C33923547 @default.
• W2615679942 hasConceptScore W2615679942C41008148 @default.
• W2615679942 hasIssue "1" @default.
• W2615679942 hasLocation W26156799421 @default.
• W2615679942 hasLocation W26156799422 @default.
• W2615679942 hasLocation W26156799423 @default.
• W2615679942 hasOpenAccess W2615679942 @default.
• W2615679942 hasPrimaryLocation W26156799421 @default.
• W2615679942 hasRelatedWork W1985579457 @default.
• W2615679942 hasRelatedWork W2056351605 @default.
• W2615679942 hasRelatedWork W2084230960 @default.
• W2615679942 hasRelatedWork W2168256183 @default.
• W2615679942 hasRelatedWork W2185537925 @default.
• W2615679942 hasRelatedWork W2963757251 @default.
• W2615679942 hasRelatedWork W2996184339 @default.
• W2615679942 hasRelatedWork W3082092122 @default.
• W2615679942 hasRelatedWork W3125006395 @default.
• W2615679942 hasRelatedWork W759769899 @default.
• W2615679942 hasVolume "30" @default.
• W2615679942 isParatext "false" @default.
• W2615679942 isRetracted "false" @default.
• W2615679942 magId "2615679942" @default.
• W2615679942 workType "article" @default.