Frames from Cosines with the Degenerate Coefficients

Rahib, Sadigova Sabina; Vahid, Mamedova Zahira

doi:10.12691/ajams-1-3-1

Cited by 3 publications

(1 citation statement)

References 5 publications

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“…The concept of 𝑡-frame is introduced and studied in [22], where 𝑡 is tensor mapping. Let us note that the approximate concepts associated with the linear mapping and related results have been introduced in [24,25]. An atomic decomposition of Lebesgue spaces in the trigonometric systems with degenerate coefficients has been studied in [24,25].…”

Section: Introductionmentioning

confidence: 99%

On a Generalization of the Hilbert Frame Generated by the Bilinear Mapping

Исмайлов

Guliyeva

Nasibov

2016

Journal of Function Spaces

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The concept ofb-frame which is a generalization of the frame in Hilbert spaces generated by the bilinear mapping is considered.b-frame operator is defined; analogues of some well-known results of frame theory are obtained in Hilbert spaces. Conditions for the existence ofb-frame in Hilbert spaces are obtained; the relationship between the definite bounded surjective operator andb-frame is also studied. The concept ofb-orthonormalb-basis is introduced.

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Section: Introductionmentioning

confidence: 99%

On a Generalization of the Hilbert Frame Generated by the Bilinear Mapping

Исмайлов

Guliyeva

Nasibov

2016

Journal of Function Spaces

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Comment on “On the Frame Properties of Degenerate System of Sines”

Shukurov¹

2017

Journal of Function Spaces

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The proof of Theorem 3.1 of the paper “On the Frame Properties of Degenerate System of Sines” (see (Bilalov and Guliyeva, 2012)) published earlier in this journal contains a gap; the reasoning given there to prove this theorem is not enough to state the validity of the mentioned theorem. To overcome this shortage we state the most general fact on the completeness of sine system which implies in particular the validity of this fact. It is shown in this note that the system{ω(t)φn(t)}, where{φn(t)}is an exponential or trigonometric (cosine or sine) systems, becomes complete in the corresponding Lebesgue spaceLp(-π,π)orLp(0,π), respectively, whenever{ω(t)φn(t)}belongs to the corresponding Lebesgue space for all indicesn(under the evident natural conditionmes⁡{t:ω(t)=0}=0). It is also shown that the same conclusion does not remain valid for, in general, any complete or complete orthonormal system{φn(t)}. Besides it, the largest class of functionsω(t)for which the system{ωtsin⁡nt}n∈Nis complete inLp(0,π)space is determined.

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Basis of the Properties of Weighted Exponential Systems With Excess

Shukurov¹

2018

Vestnik of Samara University. Natural Science Series

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The main aim of this paper is the determination of a class of such functions for which a weighted exponential system becomes complete and minimal in appropriate space when exactly one of its terms is eliminated. It is shown that the system, obtained in this way cannot be a Schouder basis in this space. The last fact shows that Muckenhoupt-type criterion for the exponential system to be the Schauder basis in Lebesgue spaces after elimination of an element does not exist. This paper generalizes the results of the paper by E.S. Golubeva.

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Frames from Cosines with the Degenerate Coefficients

Cited by 3 publications

References 5 publications

On a Generalization of the Hilbert Frame Generated by the Bilinear Mapping

On a Generalization of the Hilbert Frame Generated by the Bilinear Mapping

Comment on “On the Frame Properties of Degenerate System of Sines”

Basis of the Properties of Weighted Exponential Systems With Excess

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