Complex and Harmonic Analysis

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 only there exist derivation-invariant that are not generated by the monomial exponentials they contain, but there are such subspaces with the property that the restriction of the differentiation operator has a void spectrum. A simple example is the space of all functions in C∞(a, b) whose Taylor coefficients vanish at a fixed point. We prove a general theorem which describes the possible spectra of the restriction of d dx to an invariant subspace and give a characterization of invariant subspaces for which the spectrum of the restriction of d dx is void. Joint work with B. Korenblum Nicola Arcozzi, University of Bologna Carleson measures for the Drury-Arveson space Abstract: We present a geometric characterization of the Carleson measures for the Drury-Arveson space, the space DA of the function f holomorphic in the unit ball B of C for which the seminorm ‖ · ‖DA is finite, ‖f‖DA = ∫ Bn ∣(1− |z|2)m+1/2f (z) ∣∣2 dz (1− |z|2)n+1 , where m is any positive integer such that 2m + 1 > n. A positive measure μ on B is Carleson for DA if DA ⊂ L(μ) continuously. Some applications will also be discussed. Joint work with R. Rochberg and E. Sawyer. Aharon Atzmon, Tel Aviv University Weighted Hardy spaces and the uncertainty principle for Fourier transforms Abstract: We associate with certain weight functions on the real line some weighted Hardy spaces and some Banach spaces of entire functions, which can be identified with closed subspaces of the corresponding weighted Lebesgue