Methods of functional analysis in operator theory and the theory of differential equations

The goal of the research team is to obtain new results in the theory of differential equations, operator theory of mathematical physics, holomorphic function theory, and frames theory, based on the application of advanced methods of functional analysis. The team members are particularly interested in the following topics: • Investigating solutions of various classes of nonlinear local and nonlocal differential equation problems. • Properties of holomorphic functions near the boundary of the domain of definition. • Various types of scattering theory (stationary, non-stationary, Lax-Phillips scattering scheme). • Studying operators of mathematical physics in Hilbert spaces with reproducing kernel. • Studying dual frames. The team's research focuses on the aforementioned topics and on collaborating with doctoral students. Since 2021, four doctoral students have defended their theses under the supervision of team members. Notably, in 2024, Ms. Paulina Pierzchała defended her doctoral dissertation with distinction, titled 'The Inverse Radon Problem for Holomorphic Functions' (supervisor: Dr. hab. P. Kot). In 2023, Dr. Radulescu, based on the scientific achievement titled 'Local and Nonlocal Issues in Nonlinear Analysis,' obtained his habilitation degree in the field of natural sciences and mathematics. The publication activity of the team members remains consistently high, with a significant contribution from Dr. hab. Radulescu, whose scientific output includes approximately 400 publications. In 2021, Dr. hab. Radulescu was listed for the fourth time among the Highly Cited Researchers (HCR) in the annual list of the world's most cited scientists. Two team members serve as editors-in-chief of journals: Professor Cojuhari for Opuscula Mathematica, and Dr. hab. Radulescu for Advances in Nonlinear Analysis. Dr. Witold Majdak serves as the managing editor of the journal Opuscula Mathematica. In 2023, the scientific journal Opuscula Mathematica achieved a Journal Impact Factor (JIF) of 1.0. In terms of JIF value, it ranked 117th out of 489 journals in the mathematics category, as listed in the Journal Citation Reports published by Clarivate Analytics. This means that Opuscula Mathematica is part of the prestigious Q1 group of journals with the highest JIF.