Abstract Harmonic Analysis on Poincare Space-time

In dealing with the non existence of solutions of partial differential operators with variable coefficients on the n-dimensional real vector group. It was customary during the last fifty years, and it still is today in larger applications, to appeal to the examples of the Lewy and Mizohata operators and Hormander condition which guarantees the non existence of solutions. A deeper understanding the nature of these kind of partial differential operators and their invariance on the Heisenberg group requires the admission of solutions. It was therefore a matter of considerable surprise to the author to discover in this book that this inference is returned in general erroneous. More precisely, the Lewy and Mizohata operators are solvable. So also the invalidity of Hormander theory for the existence. So this book opens a new way in abstract harmonic analysis on non abelian Lie groups for Mathematicians and Physicists. They will find their enjoyable with the modern construction in this book, which starts the Mathematical world by exhibiting unexpected a new groups