Nigar Aslanova - Academia.edu (original) (raw)

Nigar Aslanova

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Papers by Nigar Aslanova

Research paper thumbnail of On spectrum and trace formula for one class of singular problems

In this paper we obtain an asymptotic formula for eigenvalues of differential operator given on t... more In this paper we obtain an asymptotic formula for eigenvalues of differential operator given on the whole axis and establish a formula for the regularized trace.

Research paper thumbnail of On selfadjoint extensions of symmetric operator with exit from space

arXiv: Functional Analysis, 2020

We investigate minimal operator corresponding to operator differential expression with exit from ... more We investigate minimal operator corresponding to operator differential expression with exit from space, study its selfadjoint extensions, also for one particular selfadjoint extension corresponding to boundary value problem with some rational function of eigenparameter in boundary condition establish asymptotics of spectrum and derive trace formula

Research paper thumbnail of On one class eigenvalue problem with eigenvalue parameter in the boundary condition at one end-point

Filomat, 2018

In the present paper we investigate the spectrum of operator corresponding to eigenvalue problem ... more In the present paper we investigate the spectrum of operator corresponding to eigenvalue problem with parameter dependent boundary condition. Trace formula for that operator is also established.

Research paper thumbnail of Some spectral properties of fourth order differential operator equation

Operators and Matrices, 2018

We consider boundary value problem for fourth order differential equation with unbounded discrete... more We consider boundary value problem for fourth order differential equation with unbounded discrete operator coefficient. One of the boundary conditions involves the λ parameter. The asymptotics of spectrum of corresponding selfadjoint operator is obtained. We also calculate the trace of that operator.

Research paper thumbnail of Eigenvalue problem associated with the fourth order differential-operator equation

Rocky Mountain Journal of Mathematics, 2018

In this paper, we investigate the boundary value problem for fourth order differential operator e... more In this paper, we investigate the boundary value problem for fourth order differential operator equations with unbounded operator coefficients and one λ-dependent boundary condition. We obtain an asymptotic formula for eigenvalues and a trace formula for the corresponding selfadjoint operator. 1. Introduction. In this paper, we investigate the boundary value problem for fourth order differential equations with unbounded operator coefficients and one λ-dependent boundary condition. The main questions to be studied are the following: (A) to establish the asymptotics of eigenvalue distribution (asymptotics of the distribution function N (λ)); (B) to derive the regularized trace formula. Eigenvalue distribution, which arises in quantum mechanics, for the Sturm-Lioville operator equation with an unbounded operator-valued coefficient having compact inverse and boundary conditions without the λ-parameter is established in [10]. The asymptotics of N (λ) for the second and nth order differential operator equations with unbounded operator coefficients are treated, for example, in [1, 3, 4, 6, 14, 15, 21]. Due to the appearance of the eigenvalue parameter in the boundary condition, the problem considered herein is not self-adjoint. By introducing the direct sum of Hilbert spaces with a new scalar product 2010 AMS Mathematics subject classification.

Research paper thumbnail of Asymptotics of eigenvalue distribution and trace formula of one singular

Research paper thumbnail of On asymptotics of eigenvalues and trace formula for second order differential operator equation

Research paper thumbnail of Formula for Second Regularized Trace of a Problem with Spectral Parameter Dependent Boundary Condition

Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics

In the paper we establish a formula for the second regularized trace of the problem generated by ... more In the paper we establish a formula for the second regularized trace of the problem generated by a Sturm – Liouville operator equation and with a spectral parameter dependent boundary condition.

Research paper thumbnail of On Generalized Regularized Trace of a Fourth-Order Differential Operator with Operator Coefficient

Ukrainian Mathematical Journal, 2014

ABSTRACT We deduce a formula for the trace of a boundary-value problem with unbounded operator co... more ABSTRACT We deduce a formula for the trace of a boundary-value problem with unbounded operator coefficient and boundary conditions depending on the parameter.

Research paper thumbnail of On spectrum and trace formula for one class of singular problems

In this paper we obtain an asymptotic formula for eigenvalues of differential operator given on t... more In this paper we obtain an asymptotic formula for eigenvalues of differential operator given on the whole axis and establish a formula for the regularized trace.

Research paper thumbnail of On selfadjoint extensions of symmetric operator with exit from space

arXiv: Functional Analysis, 2020

We investigate minimal operator corresponding to operator differential expression with exit from ... more We investigate minimal operator corresponding to operator differential expression with exit from space, study its selfadjoint extensions, also for one particular selfadjoint extension corresponding to boundary value problem with some rational function of eigenparameter in boundary condition establish asymptotics of spectrum and derive trace formula

Research paper thumbnail of On one class eigenvalue problem with eigenvalue parameter in the boundary condition at one end-point

Filomat, 2018

In the present paper we investigate the spectrum of operator corresponding to eigenvalue problem ... more In the present paper we investigate the spectrum of operator corresponding to eigenvalue problem with parameter dependent boundary condition. Trace formula for that operator is also established.

Research paper thumbnail of Some spectral properties of fourth order differential operator equation

Operators and Matrices, 2018

We consider boundary value problem for fourth order differential equation with unbounded discrete... more We consider boundary value problem for fourth order differential equation with unbounded discrete operator coefficient. One of the boundary conditions involves the λ parameter. The asymptotics of spectrum of corresponding selfadjoint operator is obtained. We also calculate the trace of that operator.

Research paper thumbnail of Eigenvalue problem associated with the fourth order differential-operator equation

Rocky Mountain Journal of Mathematics, 2018

In this paper, we investigate the boundary value problem for fourth order differential operator e... more In this paper, we investigate the boundary value problem for fourth order differential operator equations with unbounded operator coefficients and one λ-dependent boundary condition. We obtain an asymptotic formula for eigenvalues and a trace formula for the corresponding selfadjoint operator. 1. Introduction. In this paper, we investigate the boundary value problem for fourth order differential equations with unbounded operator coefficients and one λ-dependent boundary condition. The main questions to be studied are the following: (A) to establish the asymptotics of eigenvalue distribution (asymptotics of the distribution function N (λ)); (B) to derive the regularized trace formula. Eigenvalue distribution, which arises in quantum mechanics, for the Sturm-Lioville operator equation with an unbounded operator-valued coefficient having compact inverse and boundary conditions without the λ-parameter is established in [10]. The asymptotics of N (λ) for the second and nth order differential operator equations with unbounded operator coefficients are treated, for example, in [1, 3, 4, 6, 14, 15, 21]. Due to the appearance of the eigenvalue parameter in the boundary condition, the problem considered herein is not self-adjoint. By introducing the direct sum of Hilbert spaces with a new scalar product 2010 AMS Mathematics subject classification.

Research paper thumbnail of Asymptotics of eigenvalue distribution and trace formula of one singular

Research paper thumbnail of On asymptotics of eigenvalues and trace formula for second order differential operator equation

Research paper thumbnail of Formula for Second Regularized Trace of a Problem with Spectral Parameter Dependent Boundary Condition

Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics

In the paper we establish a formula for the second regularized trace of the problem generated by ... more In the paper we establish a formula for the second regularized trace of the problem generated by a Sturm – Liouville operator equation and with a spectral parameter dependent boundary condition.

Research paper thumbnail of On Generalized Regularized Trace of a Fourth-Order Differential Operator with Operator Coefficient

Ukrainian Mathematical Journal, 2014

ABSTRACT We deduce a formula for the trace of a boundary-value problem with unbounded operator co... more ABSTRACT We deduce a formula for the trace of a boundary-value problem with unbounded operator coefficient and boundary conditions depending on the parameter.

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