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AUTHOR(S): Boris Osilenker
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TITLE Fourier-Sobolev Series in Continuous-Discrete Orthogonal Sobolev Polynomials |
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ABSTRACT The article studies Fourier series in continuous-discrete Sobolev spaces. The questions about the behavior of partial sums and linear means for Fourier series in orthonormal Sobolev polynomials {𝑞̂𝑛(𝑥)}(𝑥∈[−1,1]; 𝑛∈ℤ+) are considered. Results on the convergence of Λ− summation methods uniformly and almost everywhere are obtained. The compact convergence of linear summation methods in the Sobolev spaces is studied. A consequence of the obtained results is linear summation methods for Fourier - Gegenbauer -Sobolev series in a discrete Sobolev space. |
KEYWORDS Sobolev polynomials, linear means, Fourier series, summation methods, continuous-discrete space, Sobolev space, Sobolev polynomials, Gegenbauer -Sobolev polynomials |
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Cite this paper Boris Osilenker. (2025) Fourier-Sobolev Series in Continuous-Discrete Orthogonal Sobolev Polynomials. International Journal of Mathematical and Computational Methods, 10, 277-282 |
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