This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of p...This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of particle interactions with external fields.展开更多
Given φ a subharmonic function on the complex plane C,with ?φdA being a doubling measure,the author studies Fock Carleson measures and some characterizations onμsuch that the induced positive Toeplitz operator T_μ...Given φ a subharmonic function on the complex plane C,with ?φdA being a doubling measure,the author studies Fock Carleson measures and some characterizations onμsuch that the induced positive Toeplitz operator T_μ is bounded or compact between the doubling Fock space F_φ~p and F_φ~∞ with 0<p≤∞,where μ is a positive Borel measure on C.展开更多
In this work, we introduce a class of Hilbert spaces Fq of entire functions on the disk , , with reproducing kernel given by the q-exponential function eq(z);and we prove some properties concerning Toeplitz operators ...In this work, we introduce a class of Hilbert spaces Fq of entire functions on the disk , , with reproducing kernel given by the q-exponential function eq(z);and we prove some properties concerning Toeplitz operators on this space. The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator Dq by and the q-Derivative operator on the Fock space Fq;and we prove that these operators are adjoint-operators and continuous from this space into itself. Lastly, we study a generalized translation operators and a Weyl commutation relations on Fq .展开更多
In this paper, we define expectation of f∈E, i.e. E(f)=f(?), accordingto Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we prove a moment identity for the Skorohod ...In this paper, we define expectation of f∈E, i.e. E(f)=f(?), accordingto Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we prove a moment identity for the Skorohod integrals aboutvacuum state.展开更多
In this paper, we define expectation of f∈F, i.e. E(f)=f(?), according to Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we derive a formula for the expectation of ...In this paper, we define expectation of f∈F, i.e. E(f)=f(?), according to Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we derive a formula for the expectation of random Hermite polynomial in Skorohod integral on Guichardet- Fock spaces. In particular, we prove that the anticipative Girsanov identities under the condition E(H<sub>x</sub>(δ(x),‖x‖<sup>2</sup>)),n≥1 on Guichardet-Fock spaces.展开更多
In this work, we introduce a class of Hilbert spaces of entire functions on the disk , 0<q<1 , with reproducing kernel given by the q-Dunkl kernel . The definition and properties of the space extend naturally th...In this work, we introduce a class of Hilbert spaces of entire functions on the disk , 0<q<1 , with reproducing kernel given by the q-Dunkl kernel . The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator Q by z and the q-Dunkl operator on the Fock space;and we prove that these operators are adjoint-operators and continuous from this space into itself.展开更多
We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators o...We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators on Fq,α .展开更多
In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator...In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism.展开更多
By using commutative C*-algebra techniques, spectrum and essential spectrum of normal weighted composition operators on the Fock space over CN are completely characterized. As an application, spectrum of self-adjoint ...By using commutative C*-algebra techniques, spectrum and essential spectrum of normal weighted composition operators on the Fock space over CN are completely characterized. As an application, spectrum of self-adjoint weighted composition operators on the Fock space are obtained also.展开更多
文摘This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of particle interactions with external fields.
基金supported by the National Natural Science Foundation of China(Nos.11601149,11771139,11571105)the Zhejiang Provincial Natural Science Foundation of China(No.LY15A010014)
文摘Given φ a subharmonic function on the complex plane C,with ?φdA being a doubling measure,the author studies Fock Carleson measures and some characterizations onμsuch that the induced positive Toeplitz operator T_μ is bounded or compact between the doubling Fock space F_φ~p and F_φ~∞ with 0<p≤∞,where μ is a positive Borel measure on C.
文摘In this work, we introduce a class of Hilbert spaces Fq of entire functions on the disk , , with reproducing kernel given by the q-exponential function eq(z);and we prove some properties concerning Toeplitz operators on this space. The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator Dq by and the q-Derivative operator on the Fock space Fq;and we prove that these operators are adjoint-operators and continuous from this space into itself. Lastly, we study a generalized translation operators and a Weyl commutation relations on Fq .
文摘In this paper, we define expectation of f∈E, i.e. E(f)=f(?), accordingto Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we prove a moment identity for the Skorohod integrals aboutvacuum state.
文摘In this paper, we define expectation of f∈F, i.e. E(f)=f(?), according to Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we derive a formula for the expectation of random Hermite polynomial in Skorohod integral on Guichardet- Fock spaces. In particular, we prove that the anticipative Girsanov identities under the condition E(H<sub>x</sub>(δ(x),‖x‖<sup>2</sup>)),n≥1 on Guichardet-Fock spaces.
文摘In this work, we introduce a class of Hilbert spaces of entire functions on the disk , 0<q<1 , with reproducing kernel given by the q-Dunkl kernel . The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator Q by z and the q-Dunkl operator on the Fock space;and we prove that these operators are adjoint-operators and continuous from this space into itself.
文摘We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators on Fq,α .
基金Supported by National Natural Science Foundation of China(10171035)Natural Science Foundation of Gansu Province(ZS021-A25-004-Z) NWNU-KJCXGC-212
文摘In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism.
基金Supported by NSFC(Grant Nos.11771401 and 11471189)
文摘By using commutative C*-algebra techniques, spectrum and essential spectrum of normal weighted composition operators on the Fock space over CN are completely characterized. As an application, spectrum of self-adjoint weighted composition operators on the Fock space are obtained also.
