Spherical monomials on affine groups. (English) Zbl 1424.43004
Summary: Spherical monomials are the building blocks of spherical spectral synthesis. In this work we exhibit the basic ideas how to describe spherical monomials on some types of affine groups using invariant differential operators. In particular, we show that if the algebra of invariant differential operators is generated by a single operator then the classes of spherical monomials and of spherical moment functions coincide.
MSC:
43A45 | Spectral synthesis on groups, semigroups, etc. |
43A90 | Harmonic analysis and spherical functions |
22D15 | Group algebras of locally compact groups |