A Homomorphic Transformation for Eigenfunctions of the Sturm Liouville Differential Operator

Properties of Sturm-Liouville Eigenfunctions and Eigenvalues

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...

Sturm-liouville Operator with General Boundary Conditions

We classify the general linear boundary conditions involving u′′, u′ and u on the boundary {a, b} so that a Sturm-Liouville operator on [a, b] has a unique self-adjoint extension on a suitable Hilbert space.

The Sturm-liouville-transformation for the Solution of Vector Partial Differential Equations

Partial differential equations (PDEs) are the conventional tool for the description of timeand space-dependent physical phenomena. Vector PDEs arise from the physical analysis of multidimensional (MD) systems in terms of potential and flux quantities. Expressing the resulting coupled PDEs in vector form facilitates the direct formulation of boundary and interface conditions in their physical co...

Spectral analysis of a self-similar Sturm-Liouville operator

In this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of understanding the spectrum of Laplace operators on unbounded finitely ramified self-similar sets. In this context, this furnishes the first example of a description of the spectral nature of the operator...