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- W2012358786 abstract "Multiple Fourier series with respect to uniformly bounded orthonormal systems (ONSs) are studied. The following results are obtained. Theorem 1. Let be a complete orthonormal system on that is uniformly bounded by on this interval, assume that , and let , where . Then there exists a function cubically diverges on some measurable subset of with . Theorem 3. For and an integer let be an arbitrary measurable subset of such that . Then there exists a complete orthonormal system on uniformly bounded by there such that the multiple Fourier series of each function with respect to the product system cubically converges to a.e. on . Definitive results in this direction are established also for incomplete uniformly bounded ONSs." @default.
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- W2012358786 date "2002-10-31" @default.
- W2012358786 modified "2023-10-16" @default.
- W2012358786 title "On sets of convergence and divergence of multiple orthogonal series" @default.
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- W2012358786 doi "https://doi.org/10.1070/sm2002v193n09abeh000678" @default.
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