Sentence examples for a compact composition from inspiring English sources

In [5], the Königs domain of a compact composition operator on the Hardy space was studied and the following result was proved.

Thus we remark that C ϕ g Open image in new window is a compact composition operator by showing that ∥ C ϕ g ( f n k − f ) ∥ Q K 2, ω ( p, q ) → 0 as k → ∞.

Electron microscopy revealed a drastically reduced β-glucan layer within pun1 ∆ cell walls and an outer mannoprotein layer of a less compact composition compared to the wild-type, together explaining the zymolyase sensitivity of mutant cells.

It is interesting to provide a function theoretic characterization of when φ induces a bounded or compact composition operator on various spaces.

Although Theorem 2.1 can be viewed as a characterization of compact composition operators C ϕ g : Q K 1, ω ( p, q ) → Q K 2, ω ( p, q ) Open image in new window, by condition (5) it is not easy to check compactness of C ϕ g Open image in new window.

Madigan and Matheson (see[2]) gave a characterization of the compact composition operators on the Bloch space ℬ Open image in new window.

We saw the most lovely of all Crivelli's, a smallish Pietà, of perfect, compact composition.

In particular, see [3] for a discussion of the Kœnigs function in relation to compact composition operators on the Hardy spaces.

Finally, by a transference principle from H2 of the unit disc, explicit examples of compact composition operators with approximation numbers decaying at essentially any sub-exponential rate can be displayed.

The study of compact composition operators was started by Schwartz, who obtained the first compactness theorem in his thesis [2], showing that the integrability of over implied the compactness of on.

We also show that this is no longer true for compact composition operators on the Dirichlet space.