TAILIEUCHUNG - New trace formula for the matrix Sturm-Liouville equation with eigenparameter dependent boundary conditions

A regularized trace formula of first order for the matrix Sturm-Liouville equation with eigenparameter in the boundary conditions is obtained. | Turkish Journal of Mathematics Research Article Turk J Math (2013) 37: 278 – 285 ¨ ITAK ˙ c TUB doi: New trace formula for the matrix Sturm-Liouville equation with eigenparameter dependent boundary conditions Chuan-Fu YANG∗ Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, People’s Republic of China Received: • Accepted: • Published Online: • Printed: Abstract: A regularized trace formula of first order for the matrix Sturm-Liouville equation with eigenparameter in the boundary conditions is obtained. Key words: Matrix Sturm-Liouville problem, eigenparameter dependent boundary conditions, trace formula 1. Introduction As is known, the trace of a finite-dimensional matrix is the sum of all the eigenvalues. But in an infinitedimensional space, in general, ordinary differential operators do not have a finite trace. Gelfand and Levitan [9] firstly obtained a trace formula for a self-adjoint Sturm-Liouville differential equation. After these studies several mathematicians were interested in developing trace formulae for different differential operators. For the scalar Sturm-Liouville problems, there is an enormous literature on estimates of large eigenvalues and regularized trace formulae which may often be computed explicitly in terms of the coefficients of operators and boundary conditions. A detailed list of publications related to the present aspect can be found in [13]. Note that the trace formulae are used in the numerical computation of the first eigenvalue of the SturmLiouville problem [6]. As a generalization of the scalar Sturm-Liouville equation, the matrix Sturm-Liouville equations were found to be important in the study of particle physics [16]. Starting with Faddeev’s study of the regularized trace formula [7], matrix Sturm-Liouville operators have raised some interesting new problems. Trace .

• Toán học
• New trace formula
• Matrix Sturm Liouville problem
• Eigenparameter dependent boundary conditions
• Trace formula
• Spectral parameter
• Sturm–Liouville problem
• Interior discontinuities
• Hochstadt–Lieberman theorem
• Boundary conditions
• Polynomially dependent on the spectral parameter
• Ion chamber
• Transfer function
• Power spectral density
• Autocorrelation function
• Cross power spectral density
• Rossi α parameter
• Neutron generation time
• Q difference equation
• Jost solution
• Spectral analysis
• Spectral singularity
• Eigenvalue parameter
• Báo cáo sinh học hay
• cách trình bày báo cáo
• báo cáo sinh học
• công trình nghiên cứu sinh học
• tài liệu về sinh học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• báo cáo khoa học
• Hill’s operator
• Eigenfunctions of Hill’s operator
• Gel’fand expansion formula
• Periodic coefficients
• Electronic Engineering
• Harmonic analysis
• Fourier transforms
• Power system parameter estimation
• Scattering function
• Sturm Liouville equations
• Finite interval
• Fractional linear
• Natural science
• Elliptic equation
• Boundary value problem
• Nonsmooth domains
• Pencil of operators