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A Second Regularized Trace Formula for a Fourth Order Differential Operator

Department of Mathematics, Yildiz Technical University, Esenler, 34220 Istanbul, Turkey
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Academic Editor: Calogero Vetro
Symmetry 2021, 13(4), 629; https://doi.org/10.3390/sym13040629
Received: 24 March 2021 / Revised: 5 April 2021 / Accepted: 7 April 2021 / Published: 9 April 2021
(This article belongs to the Section Mathematics and Symmetry/Asymmetry)
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. View Full-Text
Keywords: self-adjoint operator; trace-class operator; spectrum; regularized trace self-adjoint operator; trace-class operator; spectrum; regularized trace
MDPI and ACS Style

Gül, E.; Ceyhan, A. A Second Regularized Trace Formula for a Fourth Order Differential Operator. Symmetry 2021, 13, 629. https://doi.org/10.3390/sym13040629

AMA Style

Gül E, Ceyhan A. A Second Regularized Trace Formula for a Fourth Order Differential Operator. Symmetry. 2021; 13(4):629. https://doi.org/10.3390/sym13040629

Chicago/Turabian Style

Gül, Erdal, and Aylan Ceyhan. 2021. "A Second Regularized Trace Formula for a Fourth Order Differential Operator" Symmetry 13, no. 4: 629. https://doi.org/10.3390/sym13040629

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