Let E be a Banach space, with unit ball BE . We study the spectrum and the essential spectrum of a composition operator on H∞(BE) determined by an analytic symbol with a fixed point in BE . We relate the spectrum of the composition operator to that of the derivative of the symbol at the fixed point. We extend a theorem of Zheng to the context of analytic symbols on the open unit ball of a Hilbe...

In their study of the spectrum of quantum layers [6], Duclos, Exner, and Krejčǐŕık proved the existence of bound states for certain quantum layers . Part of their motivations to study the quantum layers is from mesoscopic physics. From the mathematical point of view, a quantum layer is a noncompact noncomplete manifold. For such a manifold, the spectrum of the Laplacian (with Dirichlet or Neuma...

The main objective of this study is estimating acceleration time history of 16 September 1978 Tabas earthquake incorporating the seismological/geological source-path and site model parameters by using finite-fault simulation approach. The method generalizes the stochastic ground-motion simulation technique, developed for point sources, to the case of finite faults. It subdivides the fault plane...

A bstract . For Sturm-Liouville operators on the half line, we show that the property of having singular, singular continuous, or pure point spectrum for a set of boundary conditions of positive measure depends only on the behavior of the potential at infinity. We also prove that existence of recurrent spectrum implies that of singular spectrum and that “almost sure” existence of L2-solutions i...

We analyze the spectrum of the generalized Schrödinger operator in L2(Rν), ν ≥ 2, with a general local, rotationally invariant singular interaction supported by an infinite family of concentric, equidistantly spaced spheres. It is shown that the essential spectrum consists of interlaced segments of the dense point and absolutely continuous character, and that the relation of their lengths at hi...

In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum, the boundary point spectrum, and the boundary length spectrum. Furthermore, we consider the boundary length and point spectrum that unifies the last two typ...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

We review some of Barry Simon’s central contributions concerning what is often called exotic spectral properties. These include phenomena such as Cantor spectrum, thick point spectrum and singular continuous spectrum.