Abstract
Let G be a compact Hausdorff group and H be a closed subgroup of G. In this paper, we show that every bounded linear operator T on is a pseudo-differential operator with the symbol σ for
. We present necessary and sufficient conditions on symbols to ensure that a bounded pseudo-differential operator on
is self-adjoint, normal and present explicit formula for their symbols. A necessary and sufficient condition is also given such that the bounded linear operators on
posses eigenvalues and eigenfunctions.
AMS Subject Classifications:
Acknowledgments
Shyam Swarup Mondal thanks IIT Guwahati for providing financial support.
Disclosure statement
No potential conflict of interest was reported by the author(s).