On equivalent bases in Banach spaces

Bilalov, B. T.; Muradov, Togrul

doi:10.1007/s11253-007-0040-1

Cited by 3 publications

(4 citation statements)

References 2 publications

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“…Subsequently, these results were generalized in the works of B.T. Bilalov [2]- [5], [10], [11]. In the work of S.R.…”

Section: Introductionmentioning

confidence: 98%

Basicity of a Perturbed System of Exponents in Lebesgue Spaces With a Variable Summability Exponent

Nasibova¹

2022

BMJ

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In this paper a system of exponents 1 is considered, where is some polynomial of degree m, m ∈ N. It is proved that under certain conditions on the exponent p (·) the basicity of this system in a Lebesgue space with a variable summability exponent Lp(·) (−π, π) depends on the coefficient αm−1 and m. Moreover, in the case of basicity, it is isomorphic to the classical system of exponents in Lp(·) (−π, π). Earlier in the case the Riesz basicity of this system in L2 (−π, π) was established by Yu.A.Kazmin

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“…Subsequently, these results were generalized in the works of B.T. Bilalov [2]- [5], [10], [11]. In the work of S.R.…”

Section: Introductionmentioning

confidence: 98%

Basicity of a Perturbed System of Exponents in Lebesgue Spaces With a Variable Summability Exponent

Nasibova¹

2022

BMJ

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“…Various methods were developed for establishing these properties. For more information, we refer the reader to [1,2,3,4,5,6,7,8,9].…”

Section: Introductionmentioning

confidence: 99%

“…This approach is well studied (see, e.g., the articles [6,7,8,9,14,15,16,17,18,19,28,29,30,31] and the monographs [13,20,21,22,23,24]). On the other hand, it is not difficult to see that the principal part { 1 ; } ∈N is not a standard (in other words, classical) system.…”

Section: Introductionmentioning

confidence: 99%

On basicity of eigenfunctions of second order discontinuous differential operator

Bilalov¹,

Gasymov²

2017

Ufimskii Matematicheskii Zhurnal

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Abstract. We consider a spectral problem for a second order discontinuous differential operator with spectral parameter in the boundary condition. We present a method for establishing the basicity of eigenfunctions for such problem. We also consider a direct expansion of a Banach space with respect to subspaces and we propose a method for constructing a basis for a space by the bases in subspaces. We also consider the cases when the bases for subspaces are isomorphic and the corresponding isomorphisms are not needed. The completeness, minimality and uniform minimality of the corresponding systems are studied. This approach has extensive applications in the spectral theory of discontinuous differential operators.

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“…For more detailed information see the monographs of R. Young [3], A. M. Sedletskii [4], Ch. Heil [5], O. Christensen [6] (and also the papers [7][8][9]) and their references. There is also the survey paper [10].…”

Section: Introductionmentioning

confidence: 99%