Discrete Models in Mathematical Analysis

The project is devoted to problems in mathematical analysis that have emerged as a result of the digital revolution. It is centered around discrete models in time-frequency analysis, discrete operators in harmonic analysis and function theory, as well as discrete models in differential equations and potential theory. Collaboration between project participants from different areas is a specific feature of the project. During the reporting period, the participants have obtained a number of important results in the theory of non-local elliptic equations and conservation laws, inverse spectral problems for discrete systems, discrete uncertainty principles, and discrete representations of signals. Novel numerical methods for Hamiltonian systems have also been developed.

The purpose of DIMMA is to work on major problems in mathematical analysis that have emerged as a result of the digital revolution. The project will be centered around time-frequency analysis, discrete operators in harmonic analysis and function theory, d iscrete models for elliptic operators including operators on graphs, discrete models in differential equations and potential theory, and numerical schemes. DIMMA aims to develop important mathematical results, but it should be stressed that each part of t he project includes problems arising in applications, most notably in signal processing, control theory, and physics. Problems on discrete models that require a concerted effort across the disciplines covered by the project will be emphasized. For in stance, results on discrete models in harmonic analysis will be used in order to analyze the convergence of numerical schemes, and results and ideas from complex analysis will be of crucial importance in the study of time-frequency analysis. Recognizing t he profound importance of synergy between different mathematical disciplines, DIMMA will through its activities and project management nurture interaction and collaboration between participants from the different areas represented in the project. The p roject will - support collaboration between the research groups in differential equations, complex and harmonic analysis, and numerical analysis - strengthen recruitment to the field in terms of new PhDs and postdoctoral fellows - expand professional net works of the participants