Journal of the
Korean Mathematical Society JKMS

The parabolic Bergman space is the set of $L^p(\lambda)$-solutions of the parabolic operator $L^{(\alpha)}$. In this paper, we study representing sequences on parabolic Bergman spaces. We establish a discrete version of the reproducing formula on parabolic Bergman spaces by using fractional derivatives of the fundamental solution of the parabolic operator.

Keywords: parabolic operator of fractional order, Bergman space, representing sequence

MSC numbers: Primary 35K05; Secondary 26A33, 26D15