Preface: Special issue on harmonic analysis, applied mathematics and engineering problems

Abstract

This special issue "Harmonic Analysis, Applied Mathematics and Engineering Problems", dedicated to 75th anniversary of Professor Lars-Erik Persson, contains papers on various topics in pure and applied mathematics including, in particular, such areas as harmonic analysis, function spaces, inequalities, homogenization theory, differential equations and some applied and engineering problems. It is well known that modern research in applied sciences is profoundly intertwined with such areas of pure mathematics as functional analysis, operator theory, and harmonic analysis. Thus, the methods and results of these areas are fundamental tools in the study of a variety of problems in applied sciences.

The increasing complexity of the mathematical models in applications requires more advanced mathematical tools. This encourages researchers to look for new dependencies and/or descriptions in the mathematical models of the phenomena under the study that could lead to a refinement of the model. On the one hand, new important achievements in functional analysis lead to progress in the theory of differential equations as mathematical models in applied sciences and thus to find a way to applications. On the other hand, the problems of physics and natural sciences formulated in the language of differential equations give rise to new directions in functional analysis and lead to the need to improve it giving in its turn rise to new theoretical breakthroughs.