On Basicity of a Certain Trigonometric System in a Weighted Lebesgue Space

Guliyeva, A. E.

doi:10.1134/s1995080222110117

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2023

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“…In [27], a sufficient condition for the basicity of the system E λ in Lebesgue spaces with a variable summability exponent is found. Similar problems have been also studied in [2,17,18,30].…”

Section: Introductionmentioning

confidence: 90%

Basicity of a perturbed system of exponents in rearrangement invariant spaces

2023

Transactions Issue Mathematics

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The paper considers a perturbed system of exponents, where the sequence {λn} is defined by the expression λn = m |Pm (n)|, and Pm (x) = x m + a m−1 x m−1 + ... + a 0 is a polynomial of the m-th degree with real coefficients. The basicity problem of this system in rearrangement invariant space X (−π, π) over the interval (−π, π) is studied. A sufficient condition for the system E λ to be a basis in X (−π, π) is found depending on m, the coefficient a m−1 , and on the Boyd indices α X and β X of the space X (−π, π). Some special cases of the space X (−π, π) are considered.

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Section: Introductionmentioning

confidence: 90%

Basicity of a perturbed system of exponents in rearrangement invariant spaces

2023

Transactions Issue Mathematics

View full text Add to dashboard Cite

show abstract

On Basicity of a Certain Trigonometric System in a Weighted Lebesgue Space

Cited by 1 publication

References 8 publications

Basicity of a perturbed system of exponents in rearrangement invariant spaces

Basicity of a perturbed system of exponents in rearrangement invariant spaces

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