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Öğe Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices(2018) Mert, Rukiye Öztürk; Al, Pembe İpek; Ismailov, Zameddin I.In this work the boundedness and compactness properties of upper triangular one-band block operator matrices in the infinite direct sum of Hilbert spaces have been studied. We also obtain the necessary and sufficient conditions when these operators belong to Schatten-von Neumann classes.Öğe Discreteness of Spectrum of Normal Differential Operators for First Order(2018) Mert, Rukiye Öztürk; Al, Pembe İpek; Yılmaz, Bülent; Ismailov, Zameddin I.In this work under the condition A?1 ? C?(H), we investigate the discreteness of spectrum of normal extensions in detail. Later on, the asymptotical behavior of eigenvalues of any normal extension has been examined.Öğe Dissipative canonical type differential operators for first order(2020) Mert, Rukiye Öztürk; Ismailov, Zameddin I.; Al, Pembe İpekIn 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.Öğe First order self-adjoint multipoint quasi-differential operators(TÜBİTAK, 2018) Öztürk Mert, Rukiye; Yılmaz, Bülent; Ismailov, Zameddin I.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. ©TÜBITAK.Öğe Maximal sectorial differential operators for first order(2015) Ismailov, Zameddin I.; Öztürk Mert, RukiyeIn this study, the maximal sectorial linear relations are described. Then, the discreteness of the spectrum of the linear maximal sectorial operators and asymptotical behavior of the eigenvalues of such operators in terms of the eigenvalues of its real part are investigated. Moreover, one result for the differential operators for first order in the Hilbert space of vector functions in finite interval is obtained.Öğe Normal extensions of a singular differential operator on the right semi-axis(Eurasian Mathematical Journal, 2014) Ismailov, Zameddin I.; Öztürk Mert, RukiyeIn this work, based on the method of Everitt-Zettl and using the Calkin-Gorbachuk method, all normal extensions of the minimal operator generated by a linear singular formally normal differential-operator expression of the first order in Hilbert spaces of vector-functions on the right semi-axis in terms of boundary values are described. Furthermore, the structure of the spectrum of these extensions is investigated. © The Eurasian National University.Öğe Normal extensions of a singular multipoint differential operator of first order(2012) Ismailov, Zameddin I.; Öztürk Mert, RukiyeMany problems arising in the modelling of processes of multi-particle quantum mechanics,in the quantum field theory,in the multipoint boundary value problems for the differential equations,in the physics of rigid bodies and ets support to study normal extension of formally narmal differential operators in direct sum of Hilbert spaces([1-3])Öğe On the spectrums of some class of selfadjoint singular differential operators(Ankara University, 2016) Ismailov, Zameddin I.; Yılmaz, Bülent; Öztürk Mert, RukiyeAbstract. In this work, based on the Everitt-Zettl and Calkin-Gorbachuk methods in terms of boundary values all selfadjoint extensions of the minimal operator generated by some linear singular multipoint symmetric differentialoperator expression for first order in the direct sum of Hilbert spaces of vectorfunctions on the right semi-axis are described. Later structure of the spectrum of these extensions is investigated.Öğe Selfadjoint extensions of a singular multipoint differential operator of first order(2013) Ismailov, Zameddin I.; Öztürk Mert, RukiyeMany problems arising in the modelling of processes of multi-particle quantum mechanics,in the quantum field theory,in the multipoint boundary value problems for the differential equations,in the physics of rigid bodies and ets support to study selfadjoint extension of symmetric differential operators in direct sum of Hilbert spaces([1-3]).
