Research Interests.

My research revolves around quite a few different but intertwined topics. A central problem on the part of mathematics lying between function theory and functional analysis is the characterization of interpolating sequences of some specific spaces of analytic function defined on some domain of the complex space, where interpolation is to interpreted in a number of different ways depending on the context.

The interest of the theory is first of all theoretical since interpolating sequences in reproducing kernel Hilbert spaces are known to give directly information about the spectrum of the multiplier algebra of such spaces . But nonetheless it turns out that such sequences are also interesting from a purely application-oriented point of view. In fact a classical control theory problem with feedback formulated appropriately is just the classical finite Nevanlinna-Pick interpolation problem by bounded analytic functions .

While the study of interpolating sequences for the H infinity algebra is more or less complete, much less is known about the multiplier algebra of the Dirichlet space, and the reason is far from superficial. The (Banach) algebra of bounded analytic functions is a uniform Banach algebra therefore a wide variety of tools forged during the last century are available, on the other hand the multiplier algebra of the Dirichlet space does not enjoy this property. Therefore in a sense our ignorance about this space reflects the deficiencies of our understanding of non uniform Banach algebras.

In my work I have studied interpolating sequences from different points of view. I have explored weaker notions of interpolation , and also interpolating sequences in a probabilistic setting. Since interpolation is a problem with many connections in other parts of mathematics I often diverge to other problems.