The regularized trace of Sturm–Liouville problem with discontinuities at two points

Hıra, Fatma; Altınışık, Nihat

doi:10.1080/17415977.2016.1197921

Cited by 4 publications

(3 citation statements)

References 25 publications

(29 reference statements)

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“…Then, several works on the regularized traces of scalar differential operators appeared (see [4][5][6][7][8][9]). The trace formulae for differential operators with operator coefficients were studied in many works [10][11][12][13][14][15][16][17][18]. Recently a second regularized trace formula was obtained in [19] for the Sturm-Liouville operator with the antiperiodic boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

A Second Regularized Trace Formula for a Fourth Order Differential Operator

Gül

Ceyhan

2021

Symmetry

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In applications, many states given for a system can be expressed by orthonormal elements, called “state elements”, taken in a separable Hilbert space (called “state space”). The exact nature of the Hilbert space depends on the system; for example, the state space for position and momentum states is the space of square-integrable functions. The symmetries of a quantum system can be represented by a class of unitary operators that act in the Hilbert space. The operators called ladder operators have the effect of lowering or raising the energy of the state. In this paper, we study the spectral properties of a self-adjoint, fourth-order differential operator with a bounded operator coefficient and establish a second regularized trace formula for this operator.

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Section: Introductionmentioning

confidence: 99%

A Second Regularized Trace Formula for a Fourth Order Differential Operator

Gül

Ceyhan

2021

Symmetry

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“…Trace formulas are used in inverse problems of spectral analysis of differential equations(see [14]) and for approximate calculation of the first eigenvalues of the related operator [1,4,5,7,9,14].…”

Section: Introductionmentioning

confidence: 99%

The second regularized trace formula for the Sturm-Liouville operator

Akgün¹,

Bayramoğlu²,

Bayramov³

2019

MMN

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“…This investigation was continued in many directions, such as Dirac systems [2][3][4], the case of continuous [5][6][7][8][9][10][11], discontinuous [12,13] or matrix Sturm-Liouville operator [14][15][16] and also Sturm-Liouville problems with retarded argument [17][18][19]. In the survey paper [20], the history and the current state of the theory of the regularized trace of the linear operators were presented.…”

Section: Introductionmentioning

confidence: 99%