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- W1966947067 abstract "Let E be an arbitrary set of positive measure in the N-dimensional cube TN=(-π,π)N⊂ℝN, N≥1, and let f(x)=0 on E. Let be some linear subspace of L1(TN). We investigate the behavior of rectangular partial sums of multiple trigonometric Fourier series of a function f on the sets E and TNE depending on smoothness of the function f (i.e. of the space ), and, as well, of structural and geometric characteristics of the set E (SGC(E)). Thus, we are describing pairs . It is convenient to formulate and investigate the posed question in terms of generalized localization almost everywhere (GL) and weak generalized localization almost everywhere (WGL). This means that for the multiple Fourier series of a function f, that equals zero on the set E, convergence almost everywhere is investigated on the set E (GL), or on some of its subsets E1⊂E, of positive measure (WGL)." @default.
- W1966947067 created "2016-06-24" @default.
- W1966947067 creator A5071855639 @default.
- W1966947067 date "2003-04-01" @default.
- W1966947067 modified "2023-09-25" @default.
- W1966947067 title "STRUCTURAL AND GEOMETRIC CHARACTERISTICS OF SETS OF CONVERGENCE AND DIVERGENCE OF MULTIPLE FOURIER SERIES OF FUNCTIONS WHICH EQUAL ZERO ON SOME SET" @default.
- W1966947067 doi "https://doi.org/10.1142/9789812796769_0030" @default.
- W1966947067 hasPublicationYear "2003" @default.
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