FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1966295516> ?p ?o ?g. }

• W1966295516 endingPage "401" @default.
• W1966295516 startingPage "401" @default.
• W1966295516 abstract "In this paper our primary interest is in developing further insight into properties of multiple trigonometric series, with emphasis on the problem of uniqueness of trigonometric series. Let E be a subset of positive (Lebesgue) measure of the k dimensional torus. The principal result is that the of a trigonometric series on E forces the boundedness of the partial sums almost everywhere on E where the system of partial sums is the one associated with the system of all rectangles situated symmetrically about the origin in the lattice plane with sides parallel to the axes. If E has a countable complement, then the partial sums are bounded at every point of E. This result implies a uniqueness theorem for double trigonometric series, namely, that if a double trigonometric series converges unrestrictedly rectangularly to zero everywhere, then all the coefficients are zero. Although uniqueness is still conjectural for dimensions greater than two, we obtain partial results and indicate lines of attack for this problem. We carry out an extensive comparison of various modes of (e.g., square, triangular, spherical, etc.). A number of examples of pathological double trigonometric series are displayed, both to accomplish this comparison and to indicate the best possible nature of some of the results on the growth of partial sums. We obtain some compatibility relationships for summability methods and finally we present a result involving the (C, a, 0) summability of multiple Fourier series. Introduction. The main interest of this paper will be the theory of multiple trigonometric series. Multiple Fourier series (the most important type of multiple trigonometric series) will be discussed only in connection with the theory of uniqueness and again in the last chapter. For the definitions of any unfamiliar terms used in the introduction the reader is referred to ?1. One of the main difficulties in multiple series arises in connection with the usual consistency theorems for summation methods. In order to maintain the validity of the typical theorem convergence implies summability, even in the case of Poisson summation one has to have the added condition that all partial sums be bounded. If one attempts to restrict himself to regular methods of forming the partial sums, it is easy to construct examples where this condition fails. However, by introducing unrestricted rectangular partial sums, of a multiple trigonometric Received by the editors January 22, 1971. AMS 1970 subject classifications. Primary 42A92, 42A48, 42A20, 42A24, 40B05; Secondary 40G10, 40A05, 40D15." @default.
• W1966295516 created "2016-06-24" @default.
• W1966295516 creator A5047898623 @default.
• W1966295516 creator A5086015449 @default.
• W1966295516 date "1972-01-01" @default.
• W1966295516 modified "2023-09-25" @default.
• W1966295516 title "Convergence, uniqueness, and summability of multiple trigonometric series" @default.
• W1966295516 cites W1487326501 @default.
• W1966295516 cites W1497277684 @default.
• W1966295516 cites W1982873710 @default.
• W1966295516 cites W1988901470 @default.
• W1966295516 cites W2012927093 @default.
• W1966295516 cites W2036421695 @default.
• W1966295516 cites W2042538227 @default.
• W1966295516 cites W2044736600 @default.
• W1966295516 cites W2054777142 @default.
• W1966295516 cites W2062966090 @default.
• W1966295516 cites W2064683409 @default.
• W1966295516 cites W2071377387 @default.
• W1966295516 cites W2081509619 @default.
• W1966295516 cites W2326470592 @default.
• W1966295516 doi "https://doi.org/10.1090/s0002-9947-1972-0300009-x" @default.
• W1966295516 hasPublicationYear "1972" @default.
• W1966295516 type Work @default.
• W1966295516 sameAs 1966295516 @default.
• W1966295516 citedByCount "41" @default.
• W1966295516 countsByYear W19662955162012 @default.
• W1966295516 countsByYear W19662955162013 @default.
• W1966295516 countsByYear W19662955162016 @default.
• W1966295516 countsByYear W19662955162017 @default.
• W1966295516 countsByYear W19662955162019 @default.
• W1966295516 countsByYear W19662955162020 @default.
• W1966295516 countsByYear W19662955162021 @default.
• W1966295516 crossrefType "journal-article" @default.
• W1966295516 hasAuthorship W1966295516A5047898623 @default.
• W1966295516 hasAuthorship W1966295516A5086015449 @default.
• W1966295516 hasBestOaLocation W19662955161 @default.
• W1966295516 hasConcept C120362076 @default.
• W1966295516 hasConcept C134306372 @default.
• W1966295516 hasConcept C143724316 @default.
• W1966295516 hasConcept C151730666 @default.
• W1966295516 hasConcept C162324750 @default.
• W1966295516 hasConcept C199343813 @default.
• W1966295516 hasConcept C207864730 @default.
• W1966295516 hasConcept C2777021972 @default.
• W1966295516 hasConcept C2777303404 @default.
• W1966295516 hasConcept C2777686260 @default.
• W1966295516 hasConcept C28826006 @default.
• W1966295516 hasConcept C29001434 @default.
• W1966295516 hasConcept C32929806 @default.
• W1966295516 hasConcept C33923547 @default.
• W1966295516 hasConcept C50522688 @default.
• W1966295516 hasConcept C71924100 @default.
• W1966295516 hasConcept C86803240 @default.
• W1966295516 hasConceptScore W1966295516C120362076 @default.
• W1966295516 hasConceptScore W1966295516C134306372 @default.
• W1966295516 hasConceptScore W1966295516C143724316 @default.
• W1966295516 hasConceptScore W1966295516C151730666 @default.
• W1966295516 hasConceptScore W1966295516C162324750 @default.
• W1966295516 hasConceptScore W1966295516C199343813 @default.
• W1966295516 hasConceptScore W1966295516C207864730 @default.
• W1966295516 hasConceptScore W1966295516C2777021972 @default.
• W1966295516 hasConceptScore W1966295516C2777303404 @default.
• W1966295516 hasConceptScore W1966295516C2777686260 @default.
• W1966295516 hasConceptScore W1966295516C28826006 @default.
• W1966295516 hasConceptScore W1966295516C29001434 @default.
• W1966295516 hasConceptScore W1966295516C32929806 @default.
• W1966295516 hasConceptScore W1966295516C33923547 @default.
• W1966295516 hasConceptScore W1966295516C50522688 @default.
• W1966295516 hasConceptScore W1966295516C71924100 @default.
• W1966295516 hasConceptScore W1966295516C86803240 @default.
• W1966295516 hasLocation W19662955161 @default.
• W1966295516 hasOpenAccess W1966295516 @default.
• W1966295516 hasPrimaryLocation W19662955161 @default.
• W1966295516 hasRelatedWork W1605419305 @default.
• W1966295516 hasRelatedWork W2000697665 @default.
• W1966295516 hasRelatedWork W2028424962 @default.
• W1966295516 hasRelatedWork W2028883544 @default.
• W1966295516 hasRelatedWork W2052415909 @default.
• W1966295516 hasRelatedWork W2243598942 @default.
• W1966295516 hasRelatedWork W2374396960 @default.
• W1966295516 hasRelatedWork W2953201992 @default.
• W1966295516 hasRelatedWork W3099844082 @default.
• W1966295516 hasRelatedWork W3154328908 @default.
• W1966295516 hasVolume "163" @default.
• W1966295516 isParatext "false" @default.
• W1966295516 isRetracted "false" @default.
• W1966295516 magId "1966295516" @default.
• W1966295516 workType "article" @default.