This paper deals with the relationship between the positivity of the Fock Toeplitz operators and their Berezin transforms. The author considers the special case of the bounded radial function φ(z) = a + be^(-α|z|^2)...This paper deals with the relationship between the positivity of the Fock Toeplitz operators and their Berezin transforms. The author considers the special case of the bounded radial function φ(z) = a + be^(-α|z|^2)+ ce^(-β|z|^2), where a, b, c are real numbers and α, β are positive numbers. For this type of φ, one can choose these parameters such that the Berezin transform of φ is a nonnegative function on the complex plane, but the corresponding Toeplitz operator Tφ is not positive on the Fock space.展开更多
Based on the relativistic principle and the postulate of universal invariant constants (c, l), all kinematic symmetries can be set up as the subsets of the Umov-Weyl-Fock-Hua transformations for the inertial motions. ...Based on the relativistic principle and the postulate of universal invariant constants (c, l), all kinematic symmetries can be set up as the subsets of the Umov-Weyl-Fock-Hua transformations for the inertial motions. These symmetries are connected to each other via combinations rather than via contractions and deformations.展开更多
基金supported by the Chongqing Natural Science Foundation of China(No.cstc 2013jj B0050)
文摘This paper deals with the relationship between the positivity of the Fock Toeplitz operators and their Berezin transforms. The author considers the special case of the bounded radial function φ(z) = a + be^(-α|z|^2)+ ce^(-β|z|^2), where a, b, c are real numbers and α, β are positive numbers. For this type of φ, one can choose these parameters such that the Berezin transform of φ is a nonnegative function on the complex plane, but the corresponding Toeplitz operator Tφ is not positive on the Fock space.
基金Supported by National Natural Science Foundation of China(Grant Nos.11471084,11301101 and 11671152)Guangzhou Higher Education Science and Technology Pro ject(Grant No.2012A018)
基金supported by the National Natural Science Foundation of China (Grant Nos. 90503002, 10701081, 10775140, 10505004, 10675019,10975141 and 10975167)the National Key Basic Research Program ofChina (Grant No. 2004CB318000Innovative Program of the Chinese Academy of Sciences (Grant No. KJCX3-SYW-S03)
文摘Based on the relativistic principle and the postulate of universal invariant constants (c, l), all kinematic symmetries can be set up as the subsets of the Umov-Weyl-Fock-Hua transformations for the inertial motions. These symmetries are connected to each other via combinations rather than via contractions and deformations.
