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Article On Pairs of ℓ-Köthe Spaces(Hacettepe University, 2010) Karapinar,E.Let ℓ be a Banach sequence space with a monotone norm {double pipe}· {double pipe} ℓ, in which the canonical system (ei) is a normalized unconditional basis. Let a = (ai), ai → ∞, λ = (λi) be sequences of positive numbers. We study the problem on isomorphic classification of pairs F = (Kℓ(exp(-1/p ai)),Kℓ(exp (-1/p ai + λi))). For this purpose, we consider the sequence of so-called m-rectangle characteristics μF m. It is shown that the system of all these characteristics is a complete quasidiagonal invariant on the class of pairs of finite-type ℓ-power series spaces. By using analytic scale and a modification of some invariants (modified compound invariants) it is proven that m-rectangular characteristics are invariant on the class of such pairs. Deriving the characteristic β̃ from the characteristic β, and using the interpolation method of analytic scale, we are able to generalize some results of Chalov, Dragilev, and Zahariuta (Pair of finite type power series spaces, Note di Mathematica 17, 121-142, 1997).Article Citation - Scopus: 1On the Derivation of Explicit Formulae for Solutions of the Wave Equation in Hyperbolic Space(Hacettepe University, 2013) Guseinov,G.S.We offer a new approach to solving the initial value problem for the wave equation in hyperbolic space in arbitrary dimensions. Our approach is based on the spectral analysis of the Laplace-Beltrami operator in hyperbolic space and some structural formulae for rapidly decreasing functions of this operator. © 2013, Hacettepe University. All rights reserved.Article Citation - Scopus: 1Reconstruction of Complex Jacobi Matrices From Spectral Data(Hacettepe University, 2009) Guseinov,G.S.In this paper, we introduce spectral data for finite order complex Jacobi matrices and investigate the inverse problem of determining the matrixfrom its spectral data. Necessary and sufficient conditions for the solvability of the inverse problem are established. An explicit procedure of reconstruction of the matrix from the spectral data is given.
