Analogs of the Luzin-Danzhu and Cantor-Lebesgue theorems for double trigonometric series |
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Authors: | V S Panferov |
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Institution: | 1. M. V. Lomonosov Moscow State University, USSR
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Abstract: | Let ∥ · ∥ be some norm in R2, Γ be the unit sphere induced in R2 by this norm, and {Aj} a sequence of disjoint subsets of R+ such that if ν ε Aj, then ν · Γ ∩ ZN ≠ Ø. For series of the form $$\sum\nolimits_{j = 1}^\infty {} \sum\nolimits_{\parallel n\parallel \in A_j } {c_n e^{2\pi _i (n_1 x_1 + n_2 x_2 )} } $$ analogs of the Luzin-Danzhu and Cantor-Lebesgue theorems are established. |
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