Sentence examples for representations defined on from inspiring English sources

For these ∗-algebras the problem of unitary classification of all representations defined on some dense invariant domain is shown to be equivalent to the unitary classification of arbitrary families of bounded self-adjoint operators.

Whether abstract letter representations are defined on the basis of sound is difficult to test in English, because of the rather complicated relation between sound and orthography.

We present novel families of wavelets and associated filterbanks for the analysis and representation of functions defined on circulant graphs.

How do these representations define our national identity?

Focus lies on the types of data (the content) and not on datatypes (the runtime representation defined in a programming language).

Recently Leng, Xu and Zhao (see [2]) gave the integral representation for continuous functionals defined on the space (C(T)) of all continuous real-valued functions on T; as an application, Shi and Liao (see [1]) also gave short solutions for the full and truncated K-moment problem.

Other perspectives include testing data-driven containment strategies based on the various contact patterns representations and understanding how the evaluation of their performance depends on the representation, in particular for the case of the novel representation defined by the contact matrix of distributions we introduced here.

The method employs a hierarchy of optimization problems defined on different representation levels.

We obtain a representation theorem for module maps defined on the algebra K(H) of compact operators.

In this article, we prove some fixed point theorems for generalized contractions defined on cyclic representation in the setting of partial metric spaces.

The classical integral representation formulas for holomorphic functions defined on pseudoconvex domains in Stein manifolds play an important role in the constructive theory of functions of several complex variables.