FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2058076847> ?p ?o ?g. }

• W2058076847 abstract "A Schauder is constructed for the space Ck(Tq) of k-times continuously differentiable functions on T , the product of q copies of the one-dimensional torus. This has the property that is also a for the spaces Cl(Tq), C2(Tq), ... Ckl(Tq), and an interpolating for C(Tq). 1. Notation and introduction. In this note we will simply say basis instead of Schauder . Let I denote the closed unit interval [0, 1]. Let T denote the interval I with the endpoints identified (i.e. T is the one-dimensional torus). For a natural number q, let f be a real-valued function on Iq or Tq. For a multi-index V= (Vl V2 ..,Vq), viE {0, 1, 2,. .}, let DVf denote the partial derivative fvlv,...vq We let Iv =v 1 vi denote the order of the partial derivative DVf. In case f is a function of a single variable, then Dmf will denote the mth derivative off, m= 1, 2, with the conventions Df= D'f and D?f=f. Let Ck(iq) denote the space of all real-valued functions on Iq for which all the partial derivatives of order no greater than k exist and are continuous. Writing this in symbols, we have Ck(lq) = {f: q -R; DVf is continuous for lvl < k} for k = 0, 1, 2, ... and q = 1, 2,.... Similarly, we have Ck(Tq) = {f: Tq -R; DVf is continuous for lv| ? k} for k = 0, 1, 2, ... andq = 1, 2,.... The linear spaces Ck(iq) and Ck(Tq) are Banach spaces when endowed with the norm Iflk(q,k)= E lDvIf II where 1. denotes the usual supremum norm and the sum extends over all multi-indices v with lvl <k. We use the natural conventions C(Tq)=C0(T), Ck(T) = Ck(Tl), etc. Ciesielski [3] and this author [7] independently resolved a problem of Banach by proving that the space Cl(12) has a basis. These proofs did not easily generalize Presented to the Society, January 22, 1971 under the title On the existence of Schauder bases in spaces Ck(Mn); received by the editors April 15, 1971 and, in revised form, July 15, 1971. AMS 1970 subject classifications. Primary 46B15, 46E15; Secondary 41A15, 46J15." @default.
• W2058076847 created "2016-06-24" @default.
• W2058076847 creator A5055057239 @default.
• W2058076847 date "1972-03-01" @default.
• W2058076847 modified "2023-09-27" @default.
• W2058076847 title "Schauder Bases in the Banach Spaces C k (T q )" @default.
• W2058076847 cites W2040579606 @default.
• W2058076847 cites W3021591933 @default.
• W2058076847 cites W779882243 @default.
• W2058076847 cites W787517479 @default.
• W2058076847 cites W990750373 @default.
• W2058076847 doi "https://doi.org/10.2307/1995888" @default.
• W2058076847 hasPublicationYear "1972" @default.
• W2058076847 type Work @default.
• W2058076847 sameAs 2058076847 @default.
• W2058076847 citedByCount "3" @default.
• W2058076847 crossrefType "journal-article" @default.
• W2058076847 hasAuthorship W2058076847A5055057239 @default.
• W2058076847 hasConcept C10138342 @default.
• W2058076847 hasConcept C114614502 @default.
• W2058076847 hasConcept C118615104 @default.
• W2058076847 hasConcept C132954091 @default.
• W2058076847 hasConcept C134306372 @default.
• W2058076847 hasConcept C162324750 @default.
• W2058076847 hasConcept C182306322 @default.
• W2058076847 hasConcept C202615002 @default.
• W2058076847 hasConcept C2778067643 @default.
• W2058076847 hasConcept C33923547 @default.
• W2058076847 hasConceptScore W2058076847C10138342 @default.
• W2058076847 hasConceptScore W2058076847C114614502 @default.
• W2058076847 hasConceptScore W2058076847C118615104 @default.
• W2058076847 hasConceptScore W2058076847C132954091 @default.
• W2058076847 hasConceptScore W2058076847C134306372 @default.
• W2058076847 hasConceptScore W2058076847C162324750 @default.
• W2058076847 hasConceptScore W2058076847C182306322 @default.
• W2058076847 hasConceptScore W2058076847C202615002 @default.
• W2058076847 hasConceptScore W2058076847C2778067643 @default.
• W2058076847 hasConceptScore W2058076847C33923547 @default.
• W2058076847 hasLocation W20580768471 @default.
• W2058076847 hasOpenAccess W2058076847 @default.
• W2058076847 hasPrimaryLocation W20580768471 @default.
• W2058076847 hasRelatedWork W1493030678 @default.
• W2058076847 hasRelatedWork W1797642757 @default.
• W2058076847 hasRelatedWork W1987549384 @default.
• W2058076847 hasRelatedWork W2017366376 @default.
• W2058076847 hasRelatedWork W2021661214 @default.
• W2058076847 hasRelatedWork W2066598517 @default.
• W2058076847 hasRelatedWork W2082242272 @default.
• W2058076847 hasRelatedWork W2130978483 @default.
• W2058076847 hasRelatedWork W2171515045 @default.
• W2058076847 hasRelatedWork W2352594740 @default.
• W2058076847 hasRelatedWork W2388728177 @default.
• W2058076847 hasRelatedWork W2460585209 @default.
• W2058076847 hasRelatedWork W2571739360 @default.
• W2058076847 hasRelatedWork W268182051 @default.
• W2058076847 hasRelatedWork W3004149568 @default.
• W2058076847 hasRelatedWork W3024762303 @default.
• W2058076847 hasRelatedWork W3143315759 @default.
• W2058076847 hasRelatedWork W3144049022 @default.
• W2058076847 hasRelatedWork W787517479 @default.
• W2058076847 hasRelatedWork W806901886 @default.
• W2058076847 isParatext "false" @default.
• W2058076847 isRetracted "false" @default.
• W2058076847 magId "2058076847" @default.
• W2058076847 workType "article" @default.