In this paper, we will examine the backward shift operator Lf = (f − f(0))/z on certain Banach spaces of analytic functions on the open unit disk D. In particular, for a (closed) subspace M for which LM ⊂M, we wish to determine the spectrum, the point spectrum, and the approximate point spectrum of L|M. In order to do this, we will use the concept of “pseudocontinuation” of functions across the...

We consider a weighted Cheeger’s constant for a graph and we examine the gap between the first two eigenvalues of Laplacian. We establish several isoperimetric inequalities concerning the unweighted Cheeger’s constant, weighted Cheeger’s constants and eigenvalues for Neumann and Dirichlet conditions .

——————————————————————————————————– Abstract In this Note, we study the characterization of the kernel of the Laplace operator with Dirichlet boundary conditions in exterior domains. We consider data in weighted Sobolev spaces. Résumé Nouvelle caractérisation du noyau du laplacien en domaine extérieur. Nous étudions dans cet article la caractérisation du noyau de l’opérateur laplacien avec des ...

The paper deals with an extension theorem by Costakis and Vlachou on simultaneous approximation for holomorphic function to the setting of Dirichlet series, which are absolutely convergent in the right half of the complex plane. The derivation operator used in the analytic case is substituted by a weighted backward shift operator in the Dirichlet case. We show the similarities and extensions in...