Mean value properties of generalised eigenfunctions

Mean Growth of Koenigs Eigenfunctions

In 1884, G. Koenigs solved Schroeder’s functional equationf ◦ φ = λf in the following context: φ is a given holomorphic function mapping the openunit disk U into itself and fixing a point a ∈ U , f is holomorphic on U , and λis a complex scalar. Koenigs showed that if 0 <|φ′(a)| < 1, then Schroeder’sequation for φ has a unique holomorphic solution σ satisfyingσ ◦ φ =...

Mean Value Properties of the Laplacian

Let <¡>(z2) be an even entire function of temperate exponential type, L a selfadjoint realization of -A + c(x), where A is the Laplace-Beltrami operator on a Riemannian manifold, and <¡>(L) the operator given by spectral theory. A PaleyWiener theorem on the support of ( L) is proved, and is used to show that Lu = \u on a suitable domain implies (L)u = <p(\)u, as well as a generalization o...

MEAN VALUE INTERPOLATION ON SPHERES

In this paper we consider   multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have   concentric spheres. Indeed, we consider the problem in three variables when it is not correct.  

Properties of Sturm-Liouville Eigenfunctions and Eigenvalues

Strong and weak mean value properties on trees

We consider the mean value properties for finite variation measures with respect to a Markov operator in a discrete environnement. We prove equivalent conditions for the weak mean value property in the case of general Markov operators and for the strong mean value property in the case of transient Markov operators adapted to a tree structure. In this last case, conditions for the equivalence be...