We derive necessary and sufficient conditions for a Hill operator (i.e., a one-dimensional periodic Schrödinger operator) H = −d/dx + V to be a spectral operator of scalar type. The conditions show the remarkable fact that the property of a Hill operator being a spectral operator is independent of smoothness (or even analyticity) properties of the potential V . In the course of our analysis we ...

This paper introduces QuanTree v1.1 and QuanLin v1.1, two Java applications available for free. (Source code included in the distribution.) Each application compiles a different type of input quantum evolution operator. The applications output a quantum circuit that is approximately equal to the input evolution operator. QuanTree compiles an input evolution operator whose Hamiltonian is proport...

In this paper, we introduce a new class of sets, namely semi*δ-open sets, using δ-open sets and the generalized closure operator. We find characterizations of semi*δ-open sets. We also define the semi*δ-interior of a subset. Further, we study some fundamental properties of semi*δ-open sets and semi*δ-interior.

In this first part of a study of ordered operator spaces, we develop the basic theory of 'ordered C*-bimodules'. A crucial role is played by 'open central tripotents', a JB*-triple variant of Akemann's notion of open projection.

We study positivity in C*-modules and operator spaces using open tripotents, and an ordered version of the 'noncommutative Shilov boundary'. Because of their independent interest, we also systematically study open tripo-tents and their properties.

We establish an integral representation of a right inverse of the Askey-Wilson finite difference operator on L2 with weight (1−x2)−1/2. The kernel of this integral operator is θ′4/θ4 and is the Riemann mapping function that maps the open unit disc conformally onto the interior of an ellipse. Running title: An Inverse Operator 1990 Mathematics Subject Classification: Primary 33D45, 42C10, Second...

The purpose of this paper is to prove existence and uniqueness theorem for solving an operator equation of the form F(x)+ G(x) = 0, where F is a Gâteaux differentiable operator and G is a Lipschitzian operator defined on an open convex subset of a Banach space. Our result extends and improves the previously known results in recent literature. 2010 Mathematics Subject Classification: 49M15, 65K10