Rank 1 transformations serve as a source of examples in ergodic theory showing variety algebraic, asymptotic, and spectral properties dynamical systems. The rank one transformation are closely related to the structure semigroup weak limits its powers. In this vein, known new constructions studied.

Finite rank perturbations of a semi-bounded self-adjoint operator A are studied in the scale of Hilbert spaces associated with A. A concept of quasi-boundary value space is used to describe self-adjoint operator realizations of regular and singular perturbations of A by the same formula. As an application the one-dimensional Schrödinger operator with generalized zero-range potential is consider...

Abstract. We analyze the behavior of the trace of the resolvent of an elliptic cone differential operator as the spectral parameter tends to infinity. The resolvent splits into two components, one associated with the minimal extension of the operator, and another, of finite rank, depending on the particular choice of domain. We give a full asymptotic expansion of the first component and expand ...

Using the Arthur-Selberg trace formula we express the index of a Dirac operator on an arithmetic quotient manifold as the integral over the index form plus a sum of orbital integrals. For the Euler operator these orbital integrals are shown to vanish for products of certain rank one spaces. In this case the index theorem looks exactly as in the compact case.

Abstract. We analyze the behavior of the trace of the resolvent of an elliptic cone differential operator as the spectral parameter tends to infinity. The resolvent splits into two components, one associated with the minimal extension of the operator, and another, of finite rank, depending on the particular choice of domain. We give a full asymptotic expansion of the first component and expand ...

Rough set is a theory of data analysis and a mathematical tool for dealing with vagueness, incompleteness, and granularity. Matroid, as a branch of mathematics, is a structure that generalizes linear independence in vector spaces. In this paper, we establish the relationships between partition matroids and rough sets through k-rank matroids. On the one hand, k-rank matroids are proposed to repr...

We establish that the Lie algebra of weight one states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank l is bounded above by the effective central charge c̃. We show that lattice vertex operator algebras may be characterized by the equalities c̃ = l = c, and in particular holomorphic lattice theories may be characterized among all holomorphic vertex operator a...