$k$th-order slant Toeplitz operators on the Fock space

Abstract

The notion of slant Toeplitz operators $B_\phi$ and $k$th-order slant Toeplitz operators $B_\phi^k$ on the Fock space is introduced and some of its properties are investigated. The Berezin transform of slant Toeplitz operator $B_\phi$ is also obtained. In addition, the commutativity of $k$th-order slant Toeplitz operators with co-analytic and harmonic symbols is discussed.