By Michael E. Taylor

This publication explores a few uncomplicated roles of Lie teams in linear research, with specific emphasis at the generalizations of the Fourier rework and the research of partial differential equations. it all started as lecture notes for a one-semester graduate path given by way of the writer in noncommutative harmonic research. it's a priceless source for either graduate scholars and school, and calls for just a heritage with Fourier research and uncomplicated sensible research, plus the 1st few chapters of a customary textual content on Lie teams. the elemental approach to noncommutative harmonic research, a generalization of Fourier research, is to synthesize operators on an area on which a Lie workforce has a unitary illustration from operators on irreducible illustration areas. even though the final learn is way from whole, this booklet covers loads of the development that has been made on vital periods of Lie teams. not like many different books on harmonic research, this booklet makes a speciality of the connection among harmonic research and partial differential equations. the writer considers many classical PDEs, fairly boundary worth difficulties for domain names with basic shapes, that express noncommutative teams of symmetries. additionally, the ebook comprises designated paintings, which has no longer formerly been released, at the harmonic research of the Heisenberg workforce and harmonic research on cones.