REVERSE CARLESON MEASURES ON GENERALIZED FOCK SPACES

In this paper,we characterize reverse Carleson measures for a class of generalized Fock spaces F^(p)_(φ),with 0<p<∞and withφsatisfying dd^(c)_(φ)■ω0.As an application of these results,we obtain several equivalent characterizations for invertible Toeplitz operators Tψ,induced by positive bounded symbols φ on F^(2)_(φ).

TOEPLITZ OPERATORS WITH POSITIVE OPERATOR-VALUED SYMBOLS ON VECTOR-VALUED GENERALIZED FOCK SPACES

In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson condition,bounded Toeplitz operators,compact Toeplitz operators,and Toeplitz operators in the Schatten-p class are all considered.

A Note on Weighted Composition Operators on the Fock Space

Based on a new characterization of bounded and compact weighted compositionoperators on the Fock space obtained by Le T （Le T. Normal and isometricweighted composition operators on the Fock space. Bull. London. Math. Soc., 2014,46： 847-856）, this paper shows that a bounded weighted composition operator onthe Fock space is a Fredholm operator if and only if it is an invertible operator, andif and only if it is a nonzero constant multiple of a unitary operator. The result isvery different from the corresponding results on the Hardy space and the Bergmanspace.

Theoretical description of electron-phonon Fock space for gapless and gapped nanowires

We study the effect of electron-phonon （e-ph） interaction on the elastic and inelastic electronic transport of a nanowire connected to two simple rigid leads within the tight-binding and harmonic approximations. The model is constructed using Green＇s function and multi-channel techniques, taking into account the local and nonlocal e-ph interactions. Then, we examine the model for the gapless （simple chain） and gapped （PA-like nanowire） systems. The results show that the tunneling conductance is improved by the e-ph interaction in both local and nonlocal regimes, while for the resonance conductance, the coherent part mainly decreases and the incoherent part increases. At the corresponding energies which depend on the phonon frequency, two dips in the elastic and two peaks in the inelastic conductance spectra appear. The reason is the absorption of the phonon by the electron in transition into inelastic channels.

Skorohod Integral at Vacuum State on Guichardet-Fock Spaces

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(Hx(δ(x),‖x‖2)),n≥1 on Guichardet-Fock spaces.

Moment Identities for Skorohod Integrals on Guichardet-Fock Spaces

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.

Levy Constrained Search in Fock Space：An Alternative Approach to Noninteger Electron Number

By extending the Levy wavefunction constrained search to Fock Space,one can define a wavefunction constrained search for electron densities in systems having noninteger number of electrons.For pure-state v-representable densities,the results are equivalent to what one would obtain with the zero-temperature grand canonical ensemble.In other cases,the wavefunction constrained search in Fock space presents an upper bound to the grand canonical ensemble functional.One advantage of the Fock-space wavefunction constrained search functional over the zero-temperature grand-canonical ensemble constrained search functional is that certain specific excited states(i.e.,those that are not ground-statev-representable) are the stationary points of the Fock-space functional.However,a potential disadvantage of the Fock-space constrained search functional is that it is not convex.

Toeplitz and Translation Operators on the q-Fock Spaces

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 .

Fock Spaces for the q-Dunkl Kernel

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.

Multiplication and Translation Operators on the Fock Spaces for the q-Modified Bessel Function

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 .

Block dual Toeplitz Operators on the Orthogonal Complements of Fock Spaces

In this paper,we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces,and the compactness of the finite sum of two dual Toeplitz operators products.The commutator and semi-commutator induced by the block dual Toeplitz operators are considered.

Integral Operators Between Fock Spaces

In this paper,the authors study the integral operator■induced by a kernel functionφ(z,·)∈F_α~∞between Fock spaces.For 1≤p≤∞,they prove that S_φ:F_α^(1)→F_α^(p)is bounded if and only if■where k_(a)is the normalized reproducing kernel of F_α^(2);and,S_φ:F_α^(1)→F_α^(p)is compact if and only if■When 1<q≤∞,it is also proved that the condition(?)is not sufficient for boundedness of S_φ:F_α^(q)→F_α^(p).In the particular case■with ■∈F^(2)_α,for 1≤q<p<∞,they show that S_φ:F^(p)_α→F^(q)_αis bounded if and only if■;for 1<p≤q<∞,they give sufficient conditions for the boundedness or compactness of the operator S^(q)_φ:F^(p)_α→F_α.

Fock正交补空间上亚正规对偶Toeplitz算子

Fock空间是由整函数构成的一类重要解析函数空间.由于与量子力学中的海森堡群表示理论相关,所以不仅在函数空间算子理论有着重要研究意义,还与量子力学的研究紧密相关.对偶Toeplitz算子也是算子理论研究内容之一,且与Toeplitz算子相互影响.算子的亚正规性,起源于Halmos的Hilbert空间问题集中的第5个问题,一直都是算子理论的重点研究内容之一.主要利用函数空间的结构和对偶Toeplitz算子的性质,刻画Fock空间的正交补空间上以(z-a)(z-b)为符号的对偶Toeplitz算子亚正规性,并得出其亚正规性等价于正规性,同时也探究了以调和多项式为符号的对偶Toeplitz算子是亚正规的一些必要条件.

Analytic Characterization for Hilbert-Schmidt Operators on Fock Space

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.

A Class of Normal Weighted Composition Operators on the Fock Space of C^n

This paper characterizes a class of normal weighted composition operators and their spectrum on the Fock space of Cn.

Schatten-p Class(0

In this paper, we discuss the Schatten-p class （0 〈 p≤∞ ） of Toeplitz operators on generalized Foek space with the symbol in positive Borel measure. It makes a great difference from other papers by using the estimates of the kernel and the weight together instead of separately estimating each other. We also get the equivalent conditions when a Toeplitz operator is in the Schatten-p class.

Weighted composition operators on the Fock space

In this paper,we study weighted composition operators on theFock space F^(2).We prove that each bounded composition operator on F^(2) is complex symmetric.This is in sharp contrast with the phenomenon on the Hardy space H^(2)(D).We characterize Hermitian weighted composition operators and algebraic weighted composition operators with degree less than or equal to two on F^(2).In addition,we investigate cyclicity and hypercyclicity of complex symmetric weighted composition operators.We also characterize those weighted compositionoperators that preserveframes,tight frames or normalized tight frames on F^(2).Finally,we study mean ergodicity and uniformly mean ergodicity of weighted composition operators.

Spectrum of Normal Weighted Composition Operators on the Fock Space Over C^N

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.

Carleson Measures and Toeplitz Operators on Doubling Fock Spaces

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.

THE CODIMENSION FORMULA ON QUASI-INVARIANT SUBSPACES OF THE FOCK SPACE

Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space.This paper gives a formula to calculate the codimension of such spaces and uses this formulato study the structure of quasi-invariant subspaces of the Fock space. Especially, as one ofapplications, it is showed that the analogue of Beurling's theorem is not true for the Fock spaceL2a (Cn ) in the case of n ≥ 2.