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Natalia P. Bondarenko - One of the best experts on this subject based on the ideXlab platform.
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Spectral data characterization for the Sturm–Liouville Operator on the star-shaped graph
Analysis and Mathematical Physics, 2020Co-Authors: Natalia P. BondarenkoAbstract:The inverse spectral problems are studied for the Sturm–Liouville Operator on the star-shaped graph and for the matrix Sturm–Liouville Operator with one boundary condition in the general self-adjoint form. We obtain necessary and sufficient conditions of solvability for these two inverse problems, and also prove their local solvability and stability.
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Spectral data characterization for the Sturm-Liouville Operator on the star-shaped graph
arXiv: Spectral Theory, 2020Co-Authors: Natalia P. BondarenkoAbstract:The inverse spectral problems are studied for the Sturm-Liouville Operator on the star-shaped graph and for the matrix Sturm-Liouville Operator with the boundary condition in the general self-adjoint form. We obtain necessary and sufficient conditions of solvability for these two inverse problems, and also prove their local solvability and stability.
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spectral analysis of the matrix sturm Liouville Operator
Boundary Value Problems, 2019Co-Authors: Natalia P. BondarenkoAbstract:The self-adjoint matrix Sturm–Liouville Operator on a finite interval with a boundary condition in general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the considered Operator. These spectral characteristics play an important role in the inverse spectral theory. Our technique is based on an analysis of analytic functions and on the contour integration in the complex plane of the spectral parameter. In addition, we adapt the obtained asymptotic formulas to the Sturm–Liouville Operators on a star-shaped graph with two different types of matching conditions.
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Spectral analysis of the matrix Sturm–Liouville Operator
Boundary Value Problems, 2019Co-Authors: Natalia P. BondarenkoAbstract:The self-adjoint matrix Sturm–Liouville Operator on a finite interval with a boundary condition in general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the considered Operator. These spectral characteristics play an important role in the inverse spectral theory. Our technique is based on an analysis of analytic functions and on the contour integration in the complex plane of the spectral parameter. In addition, we adapt the obtained asymptotic formulas to the Sturm–Liouville Operators on a star-shaped graph with two different types of matching conditions.
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Spectral data asymptotics for the matrix Sturm-Liouville Operator
arXiv: Spectral Theory, 2019Co-Authors: Natalia P. BondarenkoAbstract:The self-adjoint matrix Sturm-Liouville Operator on a finite interval with a boundary condition in the general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the considered Operator. These spectral characteristics play an important role in the inverse spectral theory. Our technique is based on analysis of analytic functions and on the contour integration in the complex plane of the spectral parameter. In addition, we adapt the obtained asymptotic formulas to the Sturm-Liouville Operators on a star-shaped graph with two different types of matching conditions.
Grigori Rozenblum - One of the best experts on this subject based on the ideXlab platform.
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eigenvalue asymptotics for the sturm Liouville Operator with potential having a strong local negative singularity
Opuscula Mathematica, 2017Co-Authors: Medet Nursultanov, Grigori RozenblumAbstract:We find asymptotic formulas for the eigenvalues of the Sturm-Liouville Operator on the finite interval, with potential having a strong negative singularity at one endpoint. This is the case of limit circle in H. Weyl sense. We establish that, unlike the case of an infinite interval, the asymptotics for positive eigenvalues does not depend on the potential and it is the same as in the regular case. The asymptotics of the negative eigenvalues may depend on the potential quite strongly, however there are always asymptotically fewer negative eigenvalues than positive ones. By unknown reasons this type of problems had not been studied previously.
A. G. Kostyuchenko - One of the best experts on this subject based on the ideXlab platform.
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Spectral asymptotics for the Sturm—Liouville Operator with point interaction
Functional Analysis and Its Applications, 2010Co-Authors: R. S. Ismagilov, A. G. KostyuchenkoAbstract:For the Sturm-Liouville Operator with point interaction, weak asymptotics of the discrete spectrum are found. A class of Operators for which zero is the unique spectrum accumulation point is specified.
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Spectral Asymptotics for the Sturm-Liouville Operator with Point Interaction ∗
Functional Analysis and Its Applications, 2010Co-Authors: R. S. Ismagilov, A. G. KostyuchenkoAbstract:For the Sturm-Liouville Operator with point interaction, weak asymptotics of the discrete spectrum are found. A class of Operators for which zero is the unique spectrum accumulation point is specified.
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spectral asymptotics for the sturm Liouville Operator with point interaction
Functional Analysis and Its Applications, 2010Co-Authors: R. S. Ismagilov, A. G. KostyuchenkoAbstract:For the Sturm-Liouville Operator with point interaction, weak asymptotics of the discrete spectrum are found. A class of Operators for which zero is the unique spectrum accumulation point is specified.
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On the asymptotics of the spectrum of a nonsemibounded vector Sturm-Liouville Operator
Functional Analysis and Its Applications, 2008Co-Authors: R. S. Ismagilov, A. G. KostyuchenkoAbstract:On the half-line, we consider a vector Sturm-Liouville Operator with a potential that is unbounded below. Asymptotic formulas for the spectrum are given. These formulas involve the eigenvalues of the matrix potential as well as the “rotational velocities” of the eigenvectors.
Lakhdar T. Rachdi - One of the best experts on this subject based on the ideXlab platform.
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Uncertainty Principle in Terms of Entropy for the Riemann–Liouville Operator
Bulletin of the Malaysian Mathematical Sciences Society, 2015Co-Authors: Besma Amri, Lakhdar T. RachdiAbstract:We prove Hausdorff–Young inequality for the Fourier transform connected with Riemann–Liouville Operator. We use this inequality to establish the uncertainty principle in terms of entropy. Next, we show that we can derive the Heisenberg–Pauli–Weyl inequality for the precedent Fourier transform.
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BECKNER LOGARITHMIC UNCERTAINTY PRINCIPLE FOR THE RIEMANN–Liouville Operator
International Journal of Mathematics, 2013Co-Authors: Besma Amri, Lakhdar T. RachdiAbstract:First, we establish the Stein–Weiss inequality for the B-Riesz potential generated by the Riemann–Liouville Operator. Next, we prove the Pitt's and Beckner logarithmic inequalities related to the connected Fourier transform.
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beckner logarithmic uncertainty principle for the riemann Liouville Operator
International Journal of Mathematics, 2013Co-Authors: Besma Amri, Lakhdar T. RachdiAbstract:First, we establish the Stein–Weiss inequality for the B-Riesz potential generated by the Riemann–Liouville Operator. Next, we prove the Pitt's and Beckner logarithmic inequalities related to the connected Fourier transform.
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The Littlewood-Paley g-function associated with the Riemann-Liouville Operator
2013Co-Authors: Besma Amri, Lakhdar T. RachdiAbstract:First, we study the Gauss and Poisson semigroups connected with the Riemann-Liouville Operator. Next, we dene and study the Littlewood-Paley g -function associated with the Riemann-Liouville Operator for which we prove the L p -boundedness for p ∈ ]1, 2].
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On the range of the Fourier transform connected with Riemann-Liouville Operator
Annales mathématiques Blaise Pascal, 2009Co-Authors: Lakhdar T. Rachdi, Ahlem RouzAbstract:We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville Operator ℛ α , α ≥ 0 and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.
Bondarenko, Natalia P. - One of the best experts on this subject based on the ideXlab platform.
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Local solvability and stability of the inverse problem for the non-self-adjoint Sturm-Liouville Operator
2020Co-Authors: Bondarenko, Natalia P.Abstract:We consider the non-self-adjoint Sturm-Liouville Operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this Operator from its eigenvalues and generalized weight numbers. We prove local solvability and stability of this inverse problem, relying on the method of spectral mappings. Possible splitting of multiple eigenvalues is taken into account
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Solving an inverse problem for the Sturm-Liouville Operator with a singular potential by Yurko's method
2020Co-Authors: Bondarenko, Natalia P.Abstract:An inverse spectral problem for the Sturm-Liouville Operator with a singular potential from the class $W_2^{-1}$ is solved by the method of spectral mappings. We prove the uniqueness theorem, develop a constructive algorithm for solution, and obtain necessary and sufficient conditions of solvability for the inverse problem in the self-adjoint and the non-self-adjoint case
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Inverse problem solution and spectral data characterization for the matrix Sturm-Liouville Operator with singular potential
2020Co-Authors: Bondarenko, Natalia P.Abstract:The matrix Sturm-Liouville Operator on a finite interval with singular potential of class $W_2^{-1}$ and the general self-adjoint boundary conditions is studied. This Operator generalizes the Sturm-Liouville Operators on geometrical graphs. We investigate the inverse problem that consists in recovering the considered Operator from the spectral data (eigenvalues and weight matrices). The inverse problem is reduced to a linear equation in a suitable Banach space, and a constructive algorithm for the inverse problem solution is developed. Moreover, we obtain the spectral data characterization for the studied Operator