ly, we may think of a differential operator ~ on M as a mapping on the smooth functions on M. That is, let C~(M) denote the space of smooth real-valued functions on M. Then 3' : C~(M) ~ C~(M). Bifurcations on Hemispheres 215 In our extension theory we consider only those operators that respect the symmetries on M and N. We define these operators as follows. There is a natural action of ISO(M) o...

Let E be a Banach lattice, T be a bounded operator on E. The Weyl essential spectrum σew(T ) of the operator T is a set σew(T ) = ∩ K∈K(E) σ(T + K), where K(E) is a set of all compact operators on E. In particular for a positive operator T next subsets of the spectrum

There has been a growing interest in the study of the notion of $alpha$-migrativity and generalizations in recent years, and it has been investigated for families of certain operators such as t-norms, t-conorms, uninorms, nullnorms.This paper is mainly devoted to investigating the migrativity equations between semi-t-operators or semi-uninorms, and Mayor's aggregation operators. The results tha...

Operator radii wp(T) for a bounded linear operator T on a Hubert space were introduced in connection with unitary p-dilations. We shall be concerned with universal estimates for the ratios wp(ST)/(wa(S)wl,(T)) for commuting operators S, T and o, p > 0. 1. All operators in this paper are bounded linear operators on a complex Hubert space §. We say an operator T belongs to the class G (0 < p < oo...

We study the semi-classical behavior of the spectral function of the Schrödinger operator with short range potential. We prove that the spectral function is a semiclassical Fourier integral operator quantizing the forward and backward Hamiltonian flow relations of the system. Under a certain geometric condition we explicitly compute the phase in an oscillatory integral representation of the spe...

Closure operators defined on various sets (set of all classical fuzzy sets, set of all semi-cuts, set of all cuts in a Q-set, etc.) are investigated and it is shown how a closure operator defined on one set can be extended to a closure operator defined on another set.

A consistent Euclidean semi classical calculation is given for the superscattering operator $ in the RST model for states with a constant flux of energy. The $ operator is CPT invariant. There is no loss of quantum coherence when the energy flux is less than a critical rate and complete loss when the energy flux is critical.