Abstract
The perturbed systems of sines, which appear when solving some partial differential equations by the Fourier method, are considered in this paper. Basis properties of these systems in weighted Sobolev spaces of functions are studied.
Highlights
When solving many problems in mathematical physics by Fourier method, there appear perturbed systems of sines and cosines of the following form:{sin(nt + α (t))}∞ n=1, (1)1 ∪ {cos(nt + α (t))}∞ n=1, (2)where α(t) = βt + γ, β, γ ∈ R are real parameters
Using Fourier method requires the study of basis properties of the above systems in Lebesgue and Sobolev spaces of functions
Our paper is devoted to the study of basis properties of these systems in weighted Sobolev spaces
Summary
The perturbed systems of sines, which appear when solving some partial differential equations by the Fourier method, are considered in this paper. Basis properties of these systems in weighted Sobolev spaces of functions are studied. When solving many problems in mathematical physics by Fourier method (see e.g., [1–4]), there appear perturbed systems of sines and cosines of the following form: Using Fourier method requires the study of basis properties of the above systems in Lebesgue and Sobolev spaces of functions.
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