ROTATION-INVARIANT $L^p$-FUNCTIONS

A. Chaiworn, P. Bunpatcharajarurn
2013 International Journal of Pure and Applied Mathematics  
This paper show that the space of rotation-invariant L p -functions with respect to a Gaussian measure can established as an even L p -space on R with respect to some non-Gaussian measure. The space of holomorphic rotation-invariant L p -functions with respect to a complex Gaussian measure can established as a holomorphic even L p -space on C with respect to some non-complex Gaussian measure. We give a condition for a rotation-invariant function which the image of the Segal-Bargmann transform
more » ... argmann transform to be in the space of holomorphic rotation-invariant L q -functions with respect to a complex Gaussian measure.
doi:10.12732/ijpam.v88i1.7 fatcat:hs65agf22faenhgn54gvmtrbtu