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Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
On Polynomially Partial-$A$-Isometric Operators, Mohamed Amine Aouichaoui, Dijana Mosic
On Polynomially Partial-$A$-Isometric Operators, Mohamed Amine Aouichaoui, Dijana Mosic
Turkish Journal of Mathematics
This paper presents a generalization of the concepts of partial-$A$-isometry and left polynomially partial isometry. Our investigation is inspired by previous work in the field [5, 30, 31]. By extending the definition of partial-$A$-isometry, we provide new insights into the properties and applications of these mathematical objects. In particular, we define the notion of left $p$-partial-$A$-isometry as a broader class of operators, including partial-$A$-isometry and left polynomially partial isometry. Some basic properties of a left $p$-partial-$A$-isometry are proven, as well as its relation with $A$-isometry. Several decompositions of a left $p$-partial-$A$-isometry are developed. We consider spectral properties and matrix representation …
Half Inverse Problems For The Impulsive Quadratic Pencil With The Discontinouty Coefficient, Rauf Ami̇rov, Sevi̇m Durak
Half Inverse Problems For The Impulsive Quadratic Pencil With The Discontinouty Coefficient, Rauf Ami̇rov, Sevi̇m Durak
Turkish Journal of Mathematics
In this paper, we study the inverse spectral problem for the quadratic differential pencils with discontinuity coefficient on $\left[ 0,\pi\right] $ with separable boundary conditions and the impulsive conditions at the point $x=\dfrac{\pi}{2}$. We prove that two potential functions on the interval $\left[ 0,\pi\right] $, and the parameters in the boundary and impulsive conditions can be determined from a sequence of eigenvalues for two cases: (i) The potentials are given on $\left( 0,\dfrac{\pi}{4}\left( 1+\alpha\right) \right) ,$ (ii) The potentials are given on $\left( \dfrac{\pi}{4}\left( 1+\alpha\right) ,\pi\right) $, where $0
Dissipative Canonical Type Differential Operators For First Order, Ruki̇ye Öztürk Mert, Zameddi̇n İsmai̇lov, Pembe İpek Al
Dissipative Canonical Type Differential Operators For First Order, Ruki̇ye Öztürk Mert, Zameddi̇n İsmai̇lov, Pembe İpek Al
Turkish Journal of Mathematics
In this paper, using the Calkin-Gorbachuk method, the general form of all maximally dissipative extensions of the minimal operator generated by the first order linear symmetric canonical type quasi-differential expression in the weighted Hilbert space of vector functions has been found. Also, the spectrum set of these extensions has been investigated.
Nonabelian Cocycles And The Spectrum Of A Symmetric Monoidal Category, Antonio M. Cegarra
Nonabelian Cocycles And The Spectrum Of A Symmetric Monoidal Category, Antonio M. Cegarra
Turkish Journal of Mathematics
We present an Eilenberg-MacLane-type description for the first, second and third spaces of the spectrum defined by a symmetric monoidal category.
Spectral Analysis Of Some Classes First-Order Normal Differential Operators, Pembe Ipek Al
Spectral Analysis Of Some Classes First-Order Normal Differential Operators, Pembe Ipek Al
Turkish Journal of Mathematics
In this paper, the general form of all normal differential operators generated by first-order linear singular differential expressions in the weighted Hilbert spaces of vector-functions on right semiaxis has been found. Later on, the spectrum set of these type extensions is investigated. Finally, the asymptotical behavior of the singular numbers of any normal extension is studied.
First Order Self-Adjoint Multipoint Quasi-Differential Operators, Ruki̇ye Öztürk Mert, Bülent Yilmaz, Zameddi̇n İsmai̇lov
First Order Self-Adjoint Multipoint Quasi-Differential Operators, Ruki̇ye Öztürk Mert, Bülent Yilmaz, Zameddi̇n İsmai̇lov
Turkish Journal of Mathematics
In this paper, using the Calkin-Gorbachuk method, the general form of all self-adjoint operators generated by first order linear singular multipoint quasi-differential expressions in the direct sum of weighted Hilbert spaces of vector functions has been found. Later on, the geometry of the spectrum set of these type extensions was researched.
The Density Theorem For Hermitian K-Theory, Mohamed Elamine Talbi
The Density Theorem For Hermitian K-Theory, Mohamed Elamine Talbi
Turkish Journal of Mathematics
Karoubi's density theorem was first proved in Benayat's thesis and then cited and used in several books and articles. As K-theory is a special case of hermitian $_{\varepsilon }L$-theory, a natural question is whether such a theorem is still true in the latter theory. The purpose of this article is to show that it is indeed the case.
Evaluation Of Spectrum Of 2-Periodic Tridiagonal-Sylvester Matrix, Emrah Kiliç, Talha Arikan
Evaluation Of Spectrum Of 2-Periodic Tridiagonal-Sylvester Matrix, Emrah Kiliç, Talha Arikan
Turkish Journal of Mathematics
The Sylvester matrix was first defined by JJ Sylvester. Some authors have studied the relationships between certain orthogonal polynomials and the determinant of the Sylvester matrix. Chu studied a generalization of the Sylvester matrix. In this paper, we introduce its $2$-periodic generalization. Then we compute its spectrum by left eigenvectors with a similarity trick.
The Trace Formula For A Differential Operator Of Fourth Order With Bounded Operator Coefficients And Two Terms, Erdal Gül
Turkish Journal of Mathematics
L Yıldız Teknik Üniversitesi Fen-Edebiyat Fakültesi Matematik Bölümü Davutpaşa Kampüsü İstanbul-TURKEY e-mail: gul@yildiz.edu.tr We investigate the spectrum of a differential operator of fourth order with bounded operator coefficients and find a formula for the trace of this operator.
On The Expansions In Eigenfunctions Of Hill's Operator, Fi̇li̇z Aras, Gusei̇n Sh Gusei̇nov
On The Expansions In Eigenfunctions Of Hill's Operator, Fi̇li̇z Aras, Gusei̇n Sh Gusei̇nov
Turkish Journal of Mathematics
In this paper we show how one can deduce the Titchmarsh expansion formula in eigenfunctions of Hill's operator from the Gel'fand expansion formula.