| Abstrakt: |
This article is the first part of a work whose main result is the following statement: if, for functions , ..., , where m 2 and the numbers p1, ..., pm ∈ (1, +∞] are such that + ... + < 1, a nonresonant condition is met (the concept introduced by the author for functions from ), p ∈ (1, +∞]) then, , where [a, b] is an n-dimensional parallelepiped, the constant C > 0 does not depend on functions Δγk ∈ , while ⊂ , 1 k m are specially constructed normalized spaces. In this article, for any spaces , , p0, p ∈ (1, +∞] and any function γ ∈ , the concept of the set of resonant points of the function γ with respect to is introduced. This set is a subset of { ∪ {∞}}n and for any trigonometric polynomial of n variables with respect to any represents the spectrum of the considered polynomial. Theorems are provided on the representation of each function γ ∈ such that its resonant set is nonempty by a sum of two functions such that the first of them belongs to ∩ , = 1 and the support of the Fourier transform of the second one is concentrated in the neighborhood of the resonant set. [ABSTRACT FROM AUTHOR] |
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