New Methods Solve Old Problems

Michael Lacey is at present Professor at Georgia Institute of Technology, Atlanta, USA. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will be Visiting Professor at the Centre for Mathematical Sciences, Lund University.

Michael Lacey is one of the leading experts in harmonic analysis in the world. Harmonic analysis is fundamental in many branches of physics, engineering, astronomy, and medicine. For example it is used in image analysis, quantum mechanics, and signal theory as well as in many areas of mathematics from number theory to differential equations.

Some of the techniques and methods of harmonic analysis have especially in recent time given a new impetus to the research of complex analysis and operator theory. As a result, several previously inaccessible problems have been solved.

Michael Lacey whose area of expertise includes integral operators, succeeded in solving several problems about the Cauchy transform, one of the most important such operators. It is possible that Professor Lacey’s methods can be extended to other related problems, and therefore his cooperation with the complex analysis and operator theory group at Lund University is a particularly promising opportunity.

In the planned project the researchers will include a study of applications of the newly developed methods to the so-called Bergman projection, an operator related to the Cauchy transform, which is of central importance in complex analysis. This would be a natural extension of the solution of a 20-year-old problem recently published by the Lund group.