This volume of the Encyclopaedia contains threecontributions in the field of complex analysis. The topicstreated are mean periodicity and convolutionequations, Yang-Mills fields and the Radon-Penrose transform, andstringtheory. The latter two have strong links with quantumfield theory and the theory of general relativity. In fact, the mathematical results described inthe book arose fromthe need of physicists to find a sound mathematical basisfor their theories. The authors present their material inthe formof surveys which provide up-to-date accounts ofcurrent research. The book will be...

The objective of this monograph is to present a coherent picture of the almost mysterious role that analytic methods and, in particular, multidimensional residue have recently played in obtaining effective estimates for problems in commutative algebra. Bezout identifies, i.e.,f1g1+...+fmgm=1, appear naturally in many problems, for example in commutative algebra in the Nullstellensatz, and in signal processing in the deconvolution problem. One way to solve them is by using explicit interpolation formulas in Cn, and these depend on the theory of multidimensional residues. The authors present...

In this part, we present a survey of mean-periodicity phenomena which arise in connection with classical questions in complex analysis, partial differential equations, and more generally, convolution equations. A common feature of the problem we shall consider is the fact that their solutions depend on tech niques and ideas from complex analysis. One finds in this way a remarkable and fruitful interplay between mean-periodicity and complex analysis. This is exactly what this part will try to explore. It is probably appropriate to stress the classical flavor of all of our treat ment. Even...

A very primitive form of this monograph has existed for about two and a half years in the form of handwritten notes of a course that Alain Y ger gave at the University of Maryland. The objective, all along, has been to present a coherent picture of the almost mysterious role that analytic methods and, in particular, multidimensional residues, have recently played in obtaining effective estimates for problems in commutative algebra 71;5]* Our original interest in the subject rested on the fact that the study of many questions in harmonic analysis, like finding all distribution solutions (or...