Some elementary Sturm theory

An Indefinite Sturm Theory

We will use the variational approach to (0.1) as described in [2] and we will stick to the notations of that paper. Given the complex n-dimensional Hermitian space (C, 〈·, ·〉), for any m ∈ N let H m := H(J,C) be the Sobolev space of all H-maps from J := [0, 1] into C. A derivative dependent Hermitian form is the form Ω(x)[u] = Pm i,j=0〈D u(x), ωi,j(x)D u(x)〉, where, each ωi,j is a smooth path o...

Some basic results in elementary number theory in function fields

Article history: Received 6 March 2015 Received in revised form 18 July 2015 Accepted 19 July 2015 Available online 10 September 2015 Communicated by David Goss

A Counterexample in Sturm-Liouville Completeness Theory

We give an example of an indefinite weight Sturm-Liouville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions but not under anti-periodic boundary conditions.

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...

Elementary Number Theory