Posn(R) and Eisenstein Series provides an introduction, requiring minimal prerequisites, to the analysis on symmetric spaces of positive definite real matrices as well as quotients of this space by the unimodular group of integral matrices. The approach is presented in very classical terms and includes material on special functions, notably gamma and Bessel functions, and focuses on certain mathematical aspects of Eisenstein series.
Posn(R) and Eisenstein Series provides an introduction, requiring minimal prerequisites, to the analysis on symmetric spaces of positive definite real matrices as well as quotients of this space by the unimodular group of integral matrices. The approach is presented in very classical terms and includes material on special functions, notably gamma and Bessel functions, and focuses on certain mathematical aspects of Eisenstein series.
GLn (R) actions on Posn(R).- Measures, Integration, and Quadratic Model.- Special Functions on Posn(R).- Invariant Differential Operators on Posn(R).- Poisson duality and zeta functions.- Eisenstein Series: First Part.- Geometric and Analytic Estimates.- Eisenstein Series: Second Part.
From the reviews of the first edition:
This book treats a family of Dirichlet series in several variables associated with positive definite quadratic forms & . The purpose of the book under review is to give a crisp version of this theory. & all of the necessary reduction theory and harmonic analysis is developed simply and efficiently. Although some of the details are, by nature, intricate, this book reduces these to a minimum and provides an accessible account to this important and beautiful area of mathematics. (Samuel James Patterson, Zentralblatt MATH, Vol. 1076, 2006)
Posn(R) and EiselS)
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