TR-Dizin İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8652

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Citation - WoS: 2
Citation - Scopus: 3
Analysis of mixed-order Caputo fractional system with nonlocal integral boundary condition
(Tubitak Scientific & Technological Research Council Turkey, 2018) Akman Yildiz, Tugba; Khodabakhshi, Neda; Baleanu, Dumitru; 56389; Matematik
This paper deals with a mixed-order Caputo fractional system with nonlocal integral boundary conditions. This study can be considered as an extension of previous studies, since the orders of the equations lie on different intervals. We discuss the existence and uniqueness of the solution using fixed point methods. We enrich the study with an example.
Citation - WoS: 7
Citation - Scopus: 6
Dirac systems with regular and singular transmission effects
(2017) Uğurlu, Ekin; 238990; Matematik
In this paper, we investigate the spectral properties of singular eigenparameter dependent dissipative problems in Weyl s limit-circle case with finite transmission conditions. In particular, these transmission conditions are assumed to be regular and singular. To analyze these problems we construct suitable Hilbert spaces with special inner products and linear operators associated with these problems. Using the equivalence of the Lax Phillips scattering function and Sz-Nagy Foia¸s characteristic functions we prove that all root vectors of these dissipative operators are complete in Hilbert spaces.
Citation - WoS: 3
Citation - Scopus: 3
Dissipative operator and its Cayley transform
(2017) Tas, Kenan; Uğurlu, Ekin; 238990; 4971; Matematik
In this paper, we investigate the spectral properties of the maximal dissipative extension of the minimal symmetric differential operator generated by a second order differential expression and dissipative and eigenparameter dependent boundary conditions. For this purpose we use the characteristic function of the maximal dissipative operator and inverse operator. This investigation is done by the characteristic function of the Cayley transform of the maximal dissipative operator, which is a completely nonunitary contraction belonging to the class C0. Using Solomyak s method we also introduce the self-adjoint dilation of the maximal dissipative operator and incoming/outgoing eigenfunctions of the dilation. Moreover, we investigate other properties of the Cayley transform of the maximal dissipative operator.
Citation - Scopus: 4
Finite groups all of whose abelian subgroups of equal order are conjugate
(2006) Waall, Robert W. Van Der; Sezer, Sezgin; 180094; Matematik
In this paper we classify the finite groups whose abelian subgroups of equal order (B*-groups) are conjugate. The classification has been achieved by means of a lot of general structure properties of B*-groups, provided in the course of the paper.
Citation - WoS: 7
Citation - Scopus: 7
Fourth order differential operators with distributional potentials
(Tubitak Scientific & Technological Research Council Turkey, 2020) Ugurlu, Ekin; Bairamov, Elgiz; 238990; Matematik
In this paper, regular and singular fourth order differential operators with distributional potentials are investigated. In particular, existence and uniqueness of solutions of the fourth order differential equations are proved, deficiency indices theory of the corresponding minimal symmetric operators are studied. These symmetric operators are considered as acting on the single and direct sum Hilbert spaces. The latter one consists of three Hilbert spaces such that a squarely integrable space and two spaces of complex numbers. Moreover all maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal symmetric operators including direct sum operators are given in the single and direct sum Hilbert spaces.
Citation - WoS: 12
Citation - Scopus: 14
Hardy—Copson type inequalities for nabla time scale calculus
(Tubitak Scientific & Technological Research Council Turkey, 2021) Kayar, Zeynep; Kaymakcalan, Billur; 109448; Matematik
This paper is devoted to the nabla unification of the discrete and continuous Hardy?Copson type inequalities. Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for the discrete, continuous, and delta cases. Moreover, these dynamic inequalities not only generalize and unify the related ones in the literature but also improve them in the special cases.
Citation - WoS: 1
Citation - Scopus: 1
Left-definite Hamiltonian systems and corresponding nested circles
(Tubitak Scientific & Technological Research Council Turkey, 2023) Ugurlu, Ekin; 238990; Matematik
This work aims to construct the Titchmarsh-Weyl M(A)-theory for an even-dimensional left-definite Hamiltonian system. For this purpose, we introduce a suitable Lagrange formula and selfadjoint boundary conditions including the spectral parameter A. Then we obtain circle equations having nesting properties. Using the intersection point belonging to all the circles we share a lower bound for the number of Dirichlet-integrable solutions of the system.
Citation - WoS: 0
Citation - Scopus: 0
On a fifth-order nonselfadjoint boundary value problem
(Tubitak Scientific & Technological Research Council Turkey, 2021) Ugurlu, Ekin; Tas, Kenan; 238990; Matematik
In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative operator. In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative
Citation - WoS: 3
Citation - Scopus: 3
On some fractional operators generated from Abel’s formula
(Tubitak Scientific & Technological Research Council Turkey, 2022) Ugurlu, Ekin; 238990; Matematik
This work aims to share some fractional integrals and derivatives containing three real parameters. The main tool to introduce such operators is the corresponding Abel's equation. Solvability conditions for the Abel's equations are shared. Semigroup property for fractional integrals are introduced. Integration by parts rule is given. Moreover, mean value theorems and related results are shared. At the end of the paper, some directions for some fractional operators are given.
Citation - WoS: 8
Citation - Scopus: 11
On the solutions of a fractional boundary value problem
(Tubitak Scientific & Technological Research Council Turkey, 2018) Ugurlu, Ekin; Baleanu, Dumitru; Tas, Kenan; 238990; 56389; 4971; Matematik
This paper is devoted to showing the existence and uniqueness of solution of a regular second-order nonlinear fractional differential equation subject to the ordinary boundary conditions. The Banach fixed point theorem is used to prove the results.
Citation - WoS: 0
Citation - Scopus: 0
Scattering and characteristic functions of a dissipative operator generated by a system of equations
(Tubitak Scientific & Technological Research Council Turkey, 2021) Bayram, Elgiz; Tas, Kenan; Ugurlu, Ekin; 4971; 238990; Matematik
In this paper, we consider a system of first-order equations with the same eigenvalue parameter together with dissipative boundary conditions. Applying Lax-Phillips scattering theory and Sz.-Nagy-Foias model operator theory we prove a completeness theorem.
Citation - WoS: 1
Citation - Scopus: 0
Singular Dirac systems in the Sobolev space
(2017) Uğurlu, Ekin; 238990; Matematik
In this paper we construct Weyl s theory for the singular left-definite Dirac systems. In particular, we prove that there exists at least one solution of the system of equations that lies in the Sobolev space. Moreover, we describe the behavior of the solution belonging to the Sobolev space around the singular point.
Citation - WoS: 3
Citation - Scopus: 2
The Lebesgue constants on projective spaces
(2021) Kushpel, Alexander; Matematik
We give the solution of a classical problem of Approximation Theory on sharp asymptotic of the Lebesgueconstants or norms of the Fourier-Laplace projections on the real projective spaces Pd(R). In particular, these resultsextend sharp asymptotic found by Fejer [2] in the case of S1in 1910 and by Gronwall [4] in 1914 in the case of S2. Thecase of spheres, Sd, complex and quaternionic projective spaces, Pd(C), Pd(H) and the Cayley elliptic plane P16(Cay)was considered by Kushpel [8].
Citation - WoS: 16
Citation - Scopus: 17
Third-order boundary value transmission problems
(Tubitak Scientific & Technological Research Council Turkey, 2019) Ugurlu, Ekin; 238990; Matematik
In this paper, we consider some third-order operators with transmission conditions. In particular, it is shown that such operators are formally symmetric in the corresponding Hilbert spaces and we introduce the resolvent operators associated with the differential operators. After showing that the eigenvalues of the problems are real and discrete we introduce some ordinary and Frechet derivatives of the eigenvalues with respect to some elements of data.
Citation - WoS: 5
Citation - Scopus: 5
Widths and entropy of sets of smooth functions on compact homogeneous manifolds
(Tubitak Scientific & Technological Research Council Turkey, 2021) Tas, Kenan; Kushpel, Alexander; Levesley, Jeremy; 279144; 4971; Matematik
We develop a general method to calculate entropy and n-widths of sets of smooth functions on an arbitrary\rcompact homogeneous Riemannian manifold Md\r. Our method is essentially based on a detailed study of geometric\rcharacteristics of norms induced by subspaces of harmonics on Md\r. This approach has been developed in the cycle\rof works [1, 2, 10–19]. The method’s possibilities are not confined to the statements proved but can be applied in\rstudying more general problems. As an application, we establish sharp orders of entropy and n-widths of Sobolev’s\rclasses Wγ\rp\r(\rMd\r)\rand their generalisations in Lq\r(\rMd\r)\rfor any 1 < p, q < ∞. In the case p, q = 1, ∞ sharp in the power\rscale estimates are presented.

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