Free quantal motion on group manifolds is considered. The Hamiltonian is given by the Laplace – Beltrami operator on the group manifold, and the purpose is to get the (Feynman’s) evolution kernel Kt. The spectral expansion, which produced a series of the representation characters for Kt in the compact case, does not exist for non-compact group, where the spectrum is not bounded. In this work re...

The statistical properties of endomorphisms under the assumption that the associated Perron– Frobenius operator is quasicompact are considered. In particular, the central limit theorem, weak invariance principle and law of the iterated logarithm for sufficiently regular observations are examined. The approach clarifies the role of the usual assumptions of ergodicity, weak mixing, and exactness....

The notion the spread of a matrix was first introduced fifty years ago in algebra. In this article, we define the spread of the shape operator by applying the same idea to submanifolds of Riemannian manifolds. We prove that the spread of shape operator is a conformal invariant for any submanifold in a Riemannian manifold. Then, we prove that, for a compact submanifold of a Riemannian manifold, ...

An algebra of bounded linear operators on a Hilbert space is called strongly compact whenever each of its bounded subsets is relatively compact in the strong operator topology. The concept is most commonly studied for two algebras associated with a single operator T : the algebra alg(T ) generated by the operator, and the operator’s commutant com(T ). This paper focuses on the strong compactnes...

We establish some versions of fixed-point theorem in a Frechet topological vector space E. The main result is that every map A BC where B is a continuous map and C is a continuous linear weakly compact operator from a closed convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has fixed-point. Based on this result, we present two versions of the Kra...

The discretization of the viscous operator in an edge-based flow solver for unstructured grids has been investigated. A compact discretization of the Laplace and thin-layer operators in the viscous terms is used with two different wall boundary conditions. Furthermore, a wide discretization of the same operators is investigated. The resulting numerical operators are all formally second order ac...

Let G be a compact Lie group acting on a compact complex manifold M . We prove a trace density formula for the G-Lefschetz number of a differential operator on M . We generalize Engeli and Felder’s recent results to orbifolds.

We present a construction of biorthogonal wavelets using a compact operator which allows to preserve or increase some properties: regularity/vanishing moments, parity, compact supported. We build then a simple algorithm which computes new filters.

An example is given of a strictly singular non-compact operator on a Hereditarily Indecomposable, reflexive, asymptotic `1 Banach space. The construction of this operator relies on the existence of transfinite c0-spreading models in the dual of the space.

We obtain sufficient conditions for a densely-defined operator on the Fock space to be bounded or compact. Under the boundedness condition we then characterize the compactness of the operator in terms of its Berezin transform.