Toeplitz quantization on Fock space

Products of Toeplitz Operators on the Fock Space

Let f and g be functions, not identically zero, in the Fock space F 2 α of C. We show that the product TfTg of Toeplitz operators on F 2 α is bounded if and only if f(z) = e q(z) and g(z) = ce−q(z), where c is a nonzero constant and q is a linear polynomial.

kTH-ORDER SLANT TOEPLITZ OPERATORS ON THE FOCK SPACE

The notion of slant Toeplitz operators Bφ and kth-order slant Toeplitz operators B φ on the Fock space is introduced and some of its properties are investigated. The Berezin transform of slant Toeplitz operator Bφ is also obtained. In addition, the commutativity of kth-order slant Toeplitz operators with co-analytic and harmonic symbols is discussed.

Toeplitz Operators on Fock Spaces

Notes on Fock Space

These notes are intended as a fairly self contained explanation of Fock space and various algebras that act on it, including a Clifford algebras, a Weyl algebra, and an affine Kac-Moody algebra. We also discuss how the various algebras are related, and in particular describe the celebrated boson-fermion correspondence. We finish by briefly discussing a deformation of Fock space, which is a repr...

Berezin–Toeplitz quantization on Lie groups

Let K be a connected compact semisimple Lie group and KC its complexification. The generalized Segal–Bargmann space for KC, is a space of square-integrable holomorphic functions on KC, with respect to a K-invariant heat kernel measure. This space is connected to the “Schrödinger” Hilbert space L(K) by a unitary map, the generalized Segal–Bargmann transform. This paper considers certain natural ...