Operator Theory On Fock Type Spaces

In this paper,we introduce a parameter function φ(z),give the suf-ficient conditions that the linear operator of weighted Fock type space Fφ2 on n-dimensional complex space Cn is a bounded operator,and give the sufficient conditions that the linear operator is a compact operator by Berezin transformation.The uncertainty principle of two self-adjoint operators and the uncertainty principle of linear operators are studied in the weighted Fock space Fφ2.The first part,we introduce some research background about the boundedness(or compactness)of operators on Fock space and the un-certainty principle,as well as the definition and properties of Fock space.The second part mainly gives the sufficient conditions that the linear operator of weighted Fock space Fα2 on complex space Cn is bounded or compact when the parameter function is φ(z)=α.The third part,the uncertainty principle of two self-adjoint operators on the weighted Fock space Fφ2 is given when the parameter function isφ(z)=z2.The fourth part mainly gives the uncertainty principle of the gener-al linear operator on the weighted Fock space Fφ2 when the parameter function is φ(z)=z2.