s of Invited Talks Alexandru Aleman, Lund University Derivation-invariant subspaces of C∞ Abstract: One motivation for the study of invariant subspaces of the differentiation operator d dx on the locally convex spaces C∞(a, b) is the fact that, as opposed to differentiation on the space of entire functions, the so-called property of spectral synthesis fails dramatically in this context. Not onl...

Abstract. We develop a theory of Lp spaces based on outer measures generated through coverings by distinguished sets. The theory includes as a special case the classical Lp theory on Euclidean spaces as well as some previously considered generalizations. The theory is a framework to describe aspects of singular integral theory, such as Carleson embedding theorems, paraproduct estimates, and T (...

It is pointed out that the method used by L. Carleson to study interpolation by bounded analytic functions applies to the study of the analogous problem for H" functions. In particular, there exist sequences of points in the unit disc which are not uniformly separated, but which are such that every l" sequence can be interpolated along this sequence by an Hv function (l^p^q^ + oo). Let (77", /"...

For every C-small perturbation B, we prove that the map (x, y) 7→ (x +a+2y, 0)+B(x, y) preserves a physical, SRB probability, for a Lebesgue positive set of parameters a. When the perturbation B is zero, this is the Jackobson theorem; when the perturbation is a small constant times (0, 1), this is the celebrated Benedicks-Carleson theorem. In particular, a new proof of the last theorems is give...

We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces Bα of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they grow at least exponentially, and this speed of convergence is only obtained for symbols which do not approach the unit circle. We also give an upper bounds and explicit an example. Mathematics Su...

The theory of Carleson measures, stopping time arguments, and atomic decompositions has been well-established in harmonic analysis. More recent is the theory of phase space analysis from the point of view of wave packets on tiles, tree selection algorithms, and tree size estimates. The purpose of this paper is to demonstrate that the two theories are in fact closely related, by taking existing ...

We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of C. In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not suitable. Several properties (the Garsia-norm equivalent theorem, Carleson measure, and so on) of BMOA spaces are extended to the operator-valued setting. Then, the operat...