Classical Fine Potential Theory

Mohamed El Kadiri is formerly a Professor of Mathematics in Mohammed 5 University in Rabat. Morocco, for more than 35 years. His research activities include classical, axiomatic and probabilistic potential theories, complex variables theory, Choquet’s theory and biharmonic functions theory. He collaborated with Bent Fuglede in a series of works on the Martin boundary of a fine domain in Rn and relative questions: integral representation of nonnegative finely harmonic functions. In his collaboration with Fuglede and with Wiegerinck on the theory of plurifinely plurisubharmonic functions, he contributed to establishing the most important properties of the latter class of functions, and to the extension of the Monge-Ampère operator for finite function in this class and to the study of maximal plurifinely plurisubharmonic functions.Bent Fuglede is formerly Professor Emeritus at the Department of Mathematical Sciences, University of Copenhagen, Denmark. His research fields include functional analysis, potential theory, classical and axiomatic potential theories, capacity theory, fine topology, finely harmonic functions, Dirichlet problem, maximum principles and complex analysis in one or more variables. Author of two books, Finely Harmonic Functions and Harmonic Maps Between Rieman Polyhedra, his works greatly influenced the development of potential theory during the second half of the 20th century.

• Background in Potential Theory.- Fundamentals of Fine Potential Theory.- Further Developments.- Fine Complex Potential Theory.

“The volume has a brief appendix … which draws attention to other results in the field that the reader may wish to know about. There is also an extensive bibliography, and a helpful symbol index in addition to the main index. This carefully written and timely monograph offers a definitive account of a recently matured and substantial field of research. I expect it to be a valued resource for researchers in potential theory, complex analysis and related fields.” (Stephen J. Gardiner, Mathematical Reviews, December, 2025)