Sentence examples for examples of operators from inspiring English sources

Examples of operators with this property are given.

We also have examples of operators ({mathcal {F}}) which are not orthogonally invariant.

In what follows we shall present some examples of operators satisfying the hypotheses of our main results.

Obviously, there are examples of operators which are not Fatou, as we show in the next example.

We remark that both the fractional integral I α and oscillatory fractional integral of Ricci and Stein [15] are examples of operators which satisfy (1.4).

In this subsection, we present various examples of operators ({mathcal {F}}), matrix functions A and associated oblique boundary operators ({mathcal {G}}) which satisfy our hypotheses.

Concrete examples of operator monotone functions are provided in [9].

We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this series, for example about whether, roughly speaking, 'weak compactness' of an operator algebra, or the lack of it, can be seen in the spectra of its elements.

See [5, 10, 33] for more information and examples of L-BFNE operators (operators in this class are also called D f -firm and BFNE).

A new example of operators with kernel satisfying (1.3) and (1.4) is called Bergman-type operator; it appeared in [13].

We close this section by exhibiting a simple example of operators A satisfying the condition ( S + ) D ( A ). Let G be a bounded open set in R N. Let 1 < p < ∞ and X = W 0 1, p ( G ). Define the two operators A 1, A 2 : X → X ∗ by 〈 A 1 u, v 〉 = ∑ i = 1 N ∫ G | ∂ u ∂ x i | p − 2 ∂ u ∂ x i ∂ v ∂ x i d x, 〈 A 2 u, v 〉 = ∫ G | u | p − 2 u v d x.