A Second Regularized Trace Formula for a Fourth Order Differential Operator


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GÜL E., Ceyhan A.

SYMMETRY-BASEL, vol.13, no.4, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.3390/sym13040629
  • Journal Name: SYMMETRY-BASEL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: self-adjoint operator, trace-class operator, spectrum, regularized trace
  • Yıldız Technical University Affiliated: Yes

Abstract

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.