Carleson Embedding Research Articles

Asymptotic properties of the vector Carleson embedding theorem

The dyadic Carleson embedding operator acting on C n -valued functions has norm at least C log n. Thus the Carleson Embedding Theorem fails for Hilbert space valued functions.

Counterexample to the infinite dimensional carleson embedding theorem

We are going to show that the classical Carleson embedding theorem fails for Hilbert space valued functions and operator measures.

Some analogs of the Carleson embedding theorem for certain Hilbetr spaces of analytic functions

The embedding theorems mentioned in the title are proved for Hilbert spaces of holomorphic and harmonic functions satisfying slow growth conditions near the boundary. Bibliography: 3 titles.

Admissibility of observation functionals

The concept of infinite-time admissibility of unbounded observation functionals is introduced. Under the assumption of exponential stability of the semigroup, it is equivalent to finite-time admissibility recently investigated in Weiss (1988 b, 1989). Necessary and sufficient criteria for admissibility are given. In particular, it is shown that the Ho-Russell-Weiss (1988 b) test for admissibility of observation functionals/control vectors can be derived in an elementary way without invoking the geometric interpretation of the Carleson measure, while the criterion in Weiss (1991) can easily be deduced from the Carleson Embedding Theorem. Some practically applicable sufficient conditions guaranteeing admissibility are discussed in § 3. The results are illustrated by a feedback system containing RLCG transmission line.