Group Algebras and Applications

  • Sundaram Thangavelu
Part of the Progress in Mathematics book series (PM, volume 159)


Even though the algebra L 1 (H n ) is not commutative, the subalgebra L 1 (H n /U(n)) of radial functions forms a commutative Banach algebra under convolution. In this chapter we study the Gelfand transform on this algebra. The Gelfand spectrum is identified with the set of all bounded U(n)-spherical functions which are given by Bessel and La-guerre functions. We also consider the Banach algebra generated by the surface measures µr and get optimal estimates for its characters, from which we proceed to study Wiener-Tauberian theorems and spherical means. We prove a one radius theorem for the spherical means using the summability result of Strichartz proved in the previous chapter. We also prove a maximal theorem for the spherical means on the Heisenberg group.


Banach Algebra Heisenberg Group Group Algebra Spherical Function Maximal Ideal Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Sundaram Thangavelu
    • 1
  1. 1.Statistics & Mathematics DivisionIndian Statistical InstituteBangaloreIndia

Personalised recommendations