Böcker av Sergio Albeverio

This book includes contributions about mathematics, physics, philosophy of science, economics and finance and resulted from the Summer School "e;Complexity and Emergence: Ideas, Methods, with a Special Attention to Economics and Finance"e; held in Lake Como School of Advanced Studies, on 22-27 July 2018.The aim of the book is to provide useful instruments from the theory of complex systems, both on the theoretical level and the methodological ones, profiting from knowledge and insights from leading experts of different communities. It moves from the volume editors' conviction that to achieve progress in understanding socio-economical as well as ecological problems of our complex word such preparation is needed, together with a critical reconsideration of our basic scientific and economical approach.The potential readers are primarily master and doctorate students of mathematics, information sciences, theoretical physics and economics, as well as research workers in those areas, who want to enlarge their spectrum of knowledge towards the area of complexity and emergence. Since ideas and methods of the theory of complex systems also apply to other areas (from engineering and architecture to biology and medicine, e.g.), students and research workers from those areas will also profit from this book.

The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained.

Covering important aspects of the theory of unitary representations of nuclear Lie groups, this reference presents the general theory of energy representations and addresses various extensions of path groups and algebras. It discusses representations of G-valued jet bundles when G is not necessarily compact.