The major topics discussed in this workshop were the Feichtinger conjecture and related questions of harmonic analysis, the corona problem for the ball B n , the weighted approximation problems, and questions related to the model spaces, to multipliers, (hyper-)cyclicity, differentiability, Bezout and Fermat equations, traces and Toeplitz operators in different function spaces. A list of open problems raised at this workshop is also included. (2010) : 26B35, 30D15, 30E10, 30H80, 31C25, 46E22,

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... L30, 47A16, 47B35, 94A12. Mathematics Subject Classification Another major topic of the meeting was the weighted approximation. J. Brennan discussed the relations between uniform rational approximation and L p -polynomial approximation. H. Hedenmalm proved a uniqueness theorem for the Fourier transforms of measures with support on a hyperbola, related to the Klein-Gordon equation. A. Poltoratski discussed the type and the gap problems in weighted L p spaces and their relations to the kernels of the Toeplitz operators. One more topic of interest during the workshop was the corona problem in B n . B. Wick discussed BM O estimates for this problem using the Koszul complex technique, whereas T. Trent presented his results on the operator version of the corona problem for some multiplier spaces on B n . R. Rochberg discussed in his talk geometrical (shape) structures associated with reproducing kernel Hilbert spaces. N. Arcozzi presented an analog of the Fefferman theorem for the Dirichlet space. K. Dyakonov presented his results on (local) abc theorems for analytic functions. R.Zarouf discussed analogs of the Kreiss resolvent condition for matrices with restrictions on the spectrum. J.-F. Olsen proved an F. and M. Riesz theorem for the Hardy space H 1 (T ∞ ). E. Saksman established the optimal estimate for the growth of the frequently hypercylcic (with respect to the differentiation operator) entire functions. Namely, he proved that for every c > 0 there exists an entire frequently hypercyclic function f such that |f (z)| ≤ c|z| −1/4 e |z| , |z| > 1. E. Abakumov discussed his results on translation cyclic vectors and generating sets in weighted p (Z) and L p (R) spaces. A. Aleksandrov presented his results on the perturbation (Hölder) smoothness of the functional calculus for the normal operators with respect to the (operator) norm and to the Schatten-von Neumann norm. A. Nicolau obtained an analog of N. Makarov's result on the differentiability if the Zygmund class for the case R d , d > 1. In particular, he proved that every function in the small Zygmund class is differentiable at a set of points of Hausdorff dimension at least 1. On Wednesday morning a problem session chaired by E. Saksman had been organized. Most of the problems discussed during that session are included at the end of this report. Further open questions were pointed out in many of the talks. This workshop was organized by Alexander Borichev (Marseille), Raymond Mortini (Metz), Nicolai Nikolski (Bordeaux) and Kristian Seip (Trondheim). Unfortunately, Raymond Mortini, Nicolai Nikolski, and Kristian Seip were unable to participate. All the participants were grateful for the hospitality and the stimulating atmosphere of the Forschungsinstitut Oberwolfach.