Approximation problems related to uncertainty principles and weights

My research plan is devoted to developing a theory which bridges the classical questions on approximation problems in de Branges-Rovnyak spaces to uncertainty principles on irreducibility in the theory of subnormal operators, and to study self-improving properties of solutions to a class of Dirichlet problems.

These projects relate to classical questions that are considered to be of fundamental importance in the field, but generally regarded as difficult, where some problems have remained open for several decades.

In a recent series of work, I have gathered preliminary research results that reveal new connections between these questions and other questions in neighboring areas of mathematics, which provide a different set of available tools at our disposal that could break some of the previous barriers.

The research plan is intended to be carried out at Universitat Autónoma de Barcelona (UAB) during the first 2-years, willingly in collaboration or along side Prof. Artur Nicolau. UAB together with its close affiliations with the Catalan Inst. for Research and Adv. Studies, together consists of a large group of world leading experts in my field of expertise.

The competitive research environment provides an optimal atmosphere for me to conduct my research plan and develop as an independent researcher.

The last year of project plan is supposed to be spent at Lund University, where these problems originated from, inspired by previous works of the research group in Lund.