A Second Regularized Trace Formula for a Fourth Order Differential Operator
Abstract
:1. Introduction
- (i)
- has a weak fourth-order derivative in interval and for every are self-adjoint trace-class operators on .
- (ii)
- (iii)
- has an orthonormal basis such that .
- (iv)
- is bounded and measurable in .
2. Some Relations about Eigenvalues and Resolvents
- (a)
- Each point of the spectrum of which is not the same as in is an isolated eigenvalue of finite multiplicity.
- (b)
- is the possible eigenvalue of of any multiplicity.
- (c)
- such that are the eigenvalues of in .
3. The Second Regularized Trace Formula
Example
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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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
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 StyleGül, 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
APA StyleGül, E., & Ceyhan, A. (2021). A Second Regularized Trace Formula for a Fourth Order Differential Operator. Symmetry, 13(4), 629. https://doi.org/10.3390/sym13040629