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Applications of Lie groups to differential equations Peter J. Olver
Publisher: Springer-Verlag

Areas including commutative normed rings and functional analysis, representation theory of Lie groups and Lie algebras, generalized functions, mathematical physics, partial differential equations, and theoretical biology. It includes a chapter dedicated to the applications of Lie group theory to solving differential equations. Applebaum, Sheffield: Spectral properties of semigroups of measures on Lie groups. There is also a good article on the subject,. Pistorius, Imperial College: Maximum increments of random walks and M. Http://www.cds.caltech.edu/~marin/pubs/KoCrDe2008.pdf. The book emphasizes the most useful aspects of Lie groups, in a way that is easy for students to acquire and to assimilate. Roeckner, Bielefeld: Self-organized criticality via stochastic partial differential equations. Chafai, Toulouse: Spectral analysis of large random Markov chains D. Krasovsky, Brunel and Imperial college: Toeplitz determinants and their applications. Applications of Lie groups to differential equations by Peter J.