Sentence examples for continuity of the composition from inspiring English sources

Moreover, if (mu(Omegabackslashtau(Omega))=0), then condition (1) is necessary for the continuity of the composition operator (c_{tau}) from (L^{Phi}(Omega)) into (L^{Psi}(Omega)).

In the last subsection, we consider the strong continuity of the composition operator semigroup induced by a one-parameter semigroup of holomorphic self-maps of (Pi^).

In connection with this, we state some sufficient conditions for equi-absolute continuity of the composition operator (c_{tau}) and the multiplication operator (M_{w}) from one Orlicz space into another.

In the case when Ω has infinite measure, we were unable to show that (8) is a necessary condition for the equi-absolute continuity of the composition operator (c_{tau}).

We are interested in finding necessary and sufficient conditions for the continuity of the composition operator (c_{tau}) from the Orlicz space (L^{Phi}(Omega)=L^{Phi}(Omega,Sigma,mu)) equipped with the Luxemburg norm into the Orlicz space (L^{Psi}(Omega)=L^{Psi}(Omega,Sigma,mu)) endowed with the corresponding Luxemburg norm.

It is shown that, in general, the Radon-Nikodým derivative (frac{d(mucirctau^{-1})}{dmu}(s)) need not belong to (L^{infty}(Omega)) to guarantee the continuity of the composition operator (c_{tau}x t)=x tau(t))) from (L^{Phi}(Omega)) into (L^{Psi}(Omega)).

Both blend systems show a similar dependence of co-phase continuity on the composition and mixing time.

Burroughs wrote his first trilogy of novels over a four-year period (1950-1953) buthehe publishing history of Junkie (1953), The Yage Letters (1963), and Queer (1985) not only confused the continuity of their composition but also shaped the identity of each text.

We study the continuity of composition operators on the classical Hardy and weighted Bergman spaces of the polydisk.

This paper studied the path component of composition operators spaces and the continuity of composition operator semigroups.

Important components of these aspects were: the teachers' role in developing seminars ('ownership'), the amount and quality of preparation materials, a non-threatening learning climate, continuity of group composition, suitability of subjects for seminar teaching, the number and quality of seminar questions, and alignment of different course activities.