Browsing by Subject "eigenfunctions"

Now showing 1 - 2 of 2

Access status: Open Access ,
Eigenvalue-eigenfunction problem for Steklov's smoothing operator and differential-difference equations of mixed type
(2013) Âkovlev, Sergej I.; Âkovleva, Valentina
It is shown that any $\mu \in \mathbb{C}$ is an infinite multiplicity eigenvalue of the Steklov smoothing operator $S_h$ acting on the space $L^1_{loc}(\mathbb{R})$. For $\mu \neq 0$ the eigenvalue-eigenfunction problem leads to studying a differential-difference equation of mixed type. An existence and uniqueness theorem is proved for this equation. Further a transformation group is defined on a countably normed space of initial functions and the spectrum of the generator of this group is studied. Some possible generalizations are pointed out.
Access status: Open Access ,
Variational characterizations for eigenfunctions of analytic self-adjoint operator functions
(2013) Katsouleas, Georgios; Maroulas, John
In this paper we consider Rellich’s diagonalization theorem for analytic self-adjoint operator functions and investigate variational principles for their eigenfunctions and interlacing statements. As an application, we present a characterization for the eigenvalues of hyperbolic operator polynomials.