Description

Mathematical analysis is a branch of mathematics that deals with the study of continuous objects and their properties. It encompasses several subfields, including the study of differential and integral calculus, differential equations (both ordinary and partial), operator theory, spectral analysis, non-standard calculus, calculus on metric spaces, perturbation problems, and more. Mathematical analysis is a very versatile field of mathematics, and its techniques find applications in almost all scientific and technological research.

Research Topics

There are four main lines of research currently underway.

• The first line of research focuses on the spectral properties of certain classes of operators and their algebraic structures. This research is also related to approximation problems in frame theory.
• The second line of research focuses on regularity properties for nonlinear partial differential equations, especially in the framework of metric spaces. The approach relies heavily on variational methods.
• The third topic concerns non-Newtonian calculus and its application to a new theory of integration. This theory can be used to solve non-local differential equations on fractals.
• Finally, the fourth line of research studies domain perturbations for linear and nonlinear boundary value problems using a new method called the "functional analytic approach."

Keywords

Spectral properties; approximation problems in frame theory; nonlinear PDEs; metric spaces; non-newtonian calculus; non-local differential equations; domain perturbations.