The FAA group has performed research in Boundary Value Problems (BVPs), Differential Equations and Inclusions, Function Spaces, Integral Equations and Transforms, and Operator Theory, as well as their applications. Namely, in 2018-2024, we have obtained relevant results on: -Besov-Morrey and Triebel-Lizorkin-Morrey spaces of variable exponents; Besov and Triebel-Lizorkin spaces on rough sets; Fractional gradient method via Psi-Hilfer derivatives; the time-fractional telegraph equation of distributed order; wave equation and the fractional Sturm-Liouville problem in higher dimension; 2-microlocal Besov and Triebel-Lizorkin spaces with variable exponents; Smoothness Morrey spaces with constant and variable exponents; variable exponent Stummel and Morrey spaces and the boundedness of operators acting on such spaces; quantitative estimates for Muckenhoupt weights with nonstandard growth; existence and multiplicity of solutions results for Dirichlet, Neumann and Robin problems, in some cases with precise sign information about these solutions, via nonsmooth variational method, and local linking arguments and by nonsmooth Morse theory; regularity of solutions to minimum problems for integral functional depending on the gradient with Lagrangean having fast growth; singular or noncompact elliptic eqs on non-commutative manifolds, Schrödinger-Poisson systems, and quasilinear elliptic systems involving Radon measures; convolution type operators (e.g. of Wiener-Hopf-Hankel type), new convolutions, new integral transforms, uncertainty principles, BVP applied to other sciences (e.g. to mechanics), stability of BVP and integral equations; dynamic non-parametric and deterministic efficiency models, considering optimization class problems and undesirable-desirable outputs. In view of this past experience, the overall future objective of CIDMA's Functional Analysis and Applications group is to continue to develop internationally competitive research (and train new researchers) in the interrelation of the areas of Functional Analysis, BVPs, Differential and Integral Equations, Function Spaces, Harmonic Analysis and Operator Theory, as well as their applications to concrete problems with industry and society (to which it has made a significant contribution in recent years).
The FAA group has an annual Workshop since 2010 and runs a biweekly seminar since 1999 during lecture time, with the concern that the majority of speakers come from outside the R&D Unit and a not negligible percentage of these do their research activities outside the country.
The group is also active in organizing international conferences and has a very significant number of international scientific collaborations (e.g., in 2019 we co-organized IWOTA2019 - International Workshop on Operator Theory and its Applications, with 471 participants). Members of FAAG are editors of several international journals (e.g. Banach Journal of Mathematical Analysis) and Staicu is Editor in Chief of Libertas Mathematica (new series).