WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 5Citation - Scopus: 5On Some Fractional Operators Generated From Abel's Formula(Tubitak Scientific & Technological Research Council Turkey, 2022) Ugurlu, EkinThis 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.Article Citation - WoS: 13Citation - Scopus: 15Hardy-Copson Type Inequalities for Nabla Time Scale Calculus(Tubitak Scientific & Technological Research Council Turkey, 2021) Kaymakcalan, Billur; Kayar, ZeynepThis 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.Article Citation - WoS: 2Citation - Scopus: 6Diamond Alpha Hardy-Copson Type Dynamic Inequalities(Hacettepe Univ, Fac Sci, 2022) Kaymakcalan, Billur; Kayar, ZeynepIn this paper two kinds of dynamic Hardy-Copson type inequalities are derived via diamond alpha integrals. The first kind consists of twelve new integral inequalities which can be considered as mixed type in the sense that these inequalities contain delta, nabla and diamond alpha integrals together. The second kind involves another twelve new inequalities, which are composed of only diamond alpha integrals, unifying delta and nabla Hardy-Copson type inequalities. Our approach is quite new due to the fact that it uses time scale calculus rather than algebra. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities into one diamond alpha Hardy-Copson type inequalities and offer new Hardy-Copson type inequalities even for the special cases.Article Citation - WoS: 3Citation - Scopus: 3Left-Definite Hamiltonian Systems and Corresponding Nested Circles(Tubitak Scientific & Technological Research Council Turkey, 2023) Ugurlu, EkinThis 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.Article Citation - WoS: 3Citation - Scopus: 3The Lebesgue Constants on Projective Spaces(Tubitak, 2021) Kushpel, AlexanderWe 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].Article Citation - WoS: 1Scattering and Characteristic Functions of a Dissipative Operator Generated by a System of Equations(Tubitak Scientific & Technological Research Council Turkey, 2021) Ugurlu, Ekin; Bayram, Elgiz; Tas, KenanIn 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.Article On a Fifth-Order Nonselfadjoint Boundary Value Problem(Tubitak Scientific & Technological Research Council Turkey, 2021) Ugurlu, Ekin; Tas, KenanIn 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 dissipativeArticle Citation - WoS: 5Citation - Scopus: 5Widths and Entropy of Sets of Smooth Functions on Compact Homogeneous Manifolds(Tubitak Scientific & Technological Research Council Turkey, 2021) Levesley, Jeremy; Tas, Kenan; Kushpel, AlexanderWe 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.Article Citation - WoS: 7Citation - Scopus: 7Fourth Order Differential Operators With Distributional Potentials(Tubitak Scientific & Technological Research Council Turkey, 2020) Bairamov, Elgiz; Ugurlu, EkinIn 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.Article Citation - WoS: 3Citation - Scopus: 3Dissipative Operator and Its Cayley Transform(2017) Tas, Kenan; Uğurlu, EkinIn 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.
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