Sentence examples for prove characterizations from inspiring English sources

We prove characterizations for exponential stability of variational difference equations using translation invariant sequence spaces and emphasize the importance of each hypothesis.

As a consequence of this generalization we prove characterizations of frames and Riesz bases of these spaces extending previous results, that were known for Rd and the lattice Zd.

All this enables us to prove characterizations of subnormality of unbounded operators having invariant domain (Theorems 37 and 39) and their further applications (Theorems 41 and 43) and a description of the complex moment problem on real algebraic curves (Theorems 52 and 56).

Characterizations that highlight specific aspects of the linkages between channel networks and resultant processes are likely to be most useful, but careless application of any characterization may prove misleading no characterization can substitute for an alert, intelligent, and well-trained observer.

We prove several characterizations of strong stability of uniformly bounded evolution families (U t,s t⩾s⩾0 of bounded operators on a Banach space X, i.e. we characterize the property limt→∞ ∥U t,s x∥=0 for all s⩾0 and all x∈X.

What examples are provided to prove this characterization?

We prove a characterization of a nonhomogeneous A-harmonic equation and describe its generalization.

In the last section, we prove a characterization result; in fact, we show that every homogeneous symmetric strict monotone mean can be seen as an element of our class of means.

The reason for this geometric restriction on M is due to the fact that such a class admits an integrable screen distribution and a symmetric Ricci tensor of M. We prove a characterization theorem for such a half lightlike submanifold.

The aim of this paper is to prove a characterization of such designs (that are constructed using projective geometries) among the class of all the quasi-symmetric designs with correct parameters and with every block a good block.

As an application of our main result, we prove a characterization of frames and Riesz sequences in L2 X) generated by the action of the unitary representation under consideration on a countable set of functions in L2 X).