Topics in Noncommutative Algebra: The Theorem of Campbell, Baker, Hausdorff and Dynkin (Lecture Notes in Mathematics, Band 2034) - Softcover

Über die Autorin bzw. den Autor

1) ERMANNO LANCONELLI: --Education and Undergraduate Studies: Dec. 1966, Universita' di Bologna (Mathematics). Career/Employment: 1975-present: Full Professor of Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy); Member of the "Accademia dell'Istituto di Bologna" and of the "Accademia delle Scienze, Lettere ed Arti di Modena". 1968-1975: Theaching Assistant at Istituto di Matematica, Universita' di Bologna. --Academic activity: Director of the Istituto di Matematica di Bologna(1978/80), Director of the Undergraduate Mathematics Program, University of Bologna (1990/1999, 2000-2002, 2006-present) Director of PHD program, University of Bologna (1986/91, 1997/2000) --INVITATIONS: -University of Minnesota, Minneapolis (USA) -University of Purdue, West La Fayette, Indiana (USA) -Temple University, Philadelphia, Pennsylvania (USA) -Rutgers University, New Brunswick, New Jersey (USA) -University of Bern, Switzerland -- Specialization main fields: Partial Differential Equations, Potential Theory --CURRENT RESEARCH INTEREST: Second order linear and nonlinear partial differential equations with non- negative characteristic form and application to complex geometry and diffusion processes. Potential Theory and Harmonic Analysis in sub-riemannian settings. Real analysis and geometric methods. --EDITORIAL BOARD: Nonlinear Differential Equations and Applications, Birkhauser. --PUBLICATIONS: More than 70 papers in refereed journals. 2) UGUZZONI FRANCESCO: --Education and Undergraduate Studies: Dec. 1994, Universita' di Bologna (Mathematics) Career/Employment: February 2000: Ph.D. in Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy). October 1998: Assistant Professor at Dipartimento di Matematica, Universita' di Bologna. --CURRENT RESEARCH INTEREST: Second order linear and nonlinear partial differential equations with non- negative characteristic form and applications. Harmonic Analysis in sub- riemannian settings. --PUBLICATIONS: About 30 papers in refereed journals. 3) ANDREA BONFIGLIOLI: --Education and Undergraduate Studies: July 1998, Universita' di Bologna (Mathematics) --Career/Employment: March 2002: Ph.D. in Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy). November 2006: Assistant Professor at Dipartimento di Matematica, Universita' di Bologna. --CURRENT RESEARCH INTEREST: Second order linear partial differential equations with non-negative characteristic form and applications. Potential Theory in stratified Lie groups. --PUBLICATIONS: About 20 papers in refereed journals.

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Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, Numerical Analysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to:
1) fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra or not) to understand and apply the statements and numerous corollaries of the main result;
2) provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view and notation;
3) provide a thorough historical background of the results, together with unknown facts about the effective early contributions by Schur, Poincaré, Pascal, Campbell, Baker, Hausdorff and Dynkin;
4) give an outlook on the applications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type);
5) quickly enable the reader, through a description of the state-of-art and open problems, to understand the modern literature concerning a theorem which, though having its roots in the beginning of the 20th century, has not ceased to provide new problems and applications.

The book assumes some undergraduate-level knowledge of algebra and analysis, but apart from that is self-contained. Part II of the monograph is devoted to the proofs of the algebraic background. The monograph may therefore provide a tool for beginners in Algebra.