In this paper we study the distribution of scattering resonances for a multi-dimensional semi-classical Schrödinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea.

In this note, we will discuss what kind of operators between C*-algebras preserves Jordan triple products

For each real α,0≤α<1, we give examples of endomorphisms in dimension one with infinite topological entropy which are α‑Hölder; and for each real p,1≤p<∞, we also give examples of endomorphisms in dimension one with infinite topological entropy which are (1,p)-Sobolev. These examples are constructed within a family of endomorphisms with infinite topological entropy and which traverse all α-Hölder and (1,p)-Sobolev classes. Finally, we also give examples of endomorphisms, also in dimension one, which lie in the big and little Zygmund classes, answering a question of M. Benedicks.

We prove that log n is an almost everywhere convergence Weyl multiplier for the orthonormal systems of non-overlapping Haar polynomials. Moreover, it is done for the general systems of martingale difference polynomials.

Let X be a compact Hausdorff space and C(X) the space of continuous functions defined on X. There are three versions of the Banach-Stone theorem. They assert that the Banach space geometry, the ring structure, and the lattice structure of C(X) determine the topological structure of X, respectively. In particular, the lattice version states that every disjointness preserving linear bijection T from C(X) onto C(Y) is a weighted composition operator Tf = h . f which provides a homeomorphism from Y onto X. In this note, we manage to use basically algebraic arguments to give this lattice version a short new proof. In this way, all three versions of the Banach-Stone theorem are unified in an algebraic framework such that different isomorphisms preserve different ideal structures of C(X).