Eigenvalues and Eigenfunctions
نویسندگان
چکیده
The article describes the eigenvalue and eigenfunction problems. Basic properties, some applications and examples in system analysis are provided.
منابع مشابه
On Generalization of Sturm-Liouville Theory for Fractional Bessel Operator
In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...
متن کاملAsymptotic Distributions of Estimators of Eigenvalues and Eigenfunctions in Functional Data
Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...
متن کاملSturm-Liouville Fuzzy Problem with Fuzzy Eigenvalue Parameter
This study is on the fuzzy eigenvalues and fuzzy eigenfunctions of the Sturm-Liouville fuzzy problem with fuzzy eigenvalue parameter. We find fuzzy eigenvalues and fuzzy eigenfunctions of the problem under the approach of Hukuhara differentiability. We solve an example. We draw the graphics of eigenfunctions. We show that eigenfunctions are valid fuzzy functions or not.
متن کاملEigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions
In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....
متن کاملOn the determination of asymptotic formula of the nodal points for the Sturm-Liouville equation with one turning point
In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.
متن کاملNumerical Analysis of Stability for Temporal Bright Solitons in a PT-Symmetric NLDC
PT-Symmetry is one of the interesting topics in quantum mechanics and optics. One of the demonstration of PT-Symmetric effects in optics is appeared in the nonlinear directional coupler (NLDC). In the paper we numerically investigate the stability of temporal bright solitons propagate in a PT-Symmetric NLDC by considering gain in bar and loss in cross. By using the analytical solutions of pertu...
متن کامل