BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS

In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.

SMALL HANKEL OPERATORS ON WEIGHTEDBERGMAN SPACES OF BOUNDED SYMMETRICDOMAINS

The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel operators h(Phi) are presented in terms of a certain integral transform of the symbol Phi.

A New Kind of Two-Fold Integration Transformation in Phase Space and Its Uses in Weyl Ordering of Operators

We propose a new two-fold integration transformation in p-q phase space∫∫^∞-∞dpdq/π e^2i（p-x）（q-y）f（p,q）≡G（x,y）,which possesses some well-behaved transformation properties. We apply this transformation to the Weyl ordering of operators, especially those Q-P ordered and P-Q ordered operators.

New decomposition of the Fresnel operator corresponding to the optical transformation in ABCD-systems

By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property we obtain new decomposition of the Fresnel operator as the product of the quadratic phase operator, the squeezing operator, and the fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.

THE COMPACTNESS OF A KIND OF GENERALIZED HANKEL OPERATORS ON THE BERGMAN SPACE OF THE UNIT BALL

This paper gives the compactness criteria for a kind of generalized Hankel operators on Bergman spaces Lpa(B) defined by M. M. Peloso.

Two-Parameter Radon Transformation of the Wigner Operator and Its Inverse

Using the technique of integration within an ordered product of operators, we reveal that a new quantum mechanical representation |x,μ,v > exsit, the eigenvector of operator μQ+vP (linear combination of coordinate Q and momentum P) with eigenvalue x, which is inherent to the two-parameter(μ,v) Radon transformation of the Wigner operator. It turns out that the projection operator |x,μ,v > < x,μ,v | is just the Radon transformation of the Wigner operator. The inverse of operator Radon transformation is also derived which indicates tomography in operator version.

New two-fold integration transformation for the Wigner operator in phase space quantum mechanics and its relation to operator ordering

Using the Weyl ordering of operators expansion formula （Hong-Yi Fan, J. Phys.A 25 （1992） 3443） this paper finds a kind of two-fold integration transformation about the Wigner operator △（ q＇,p） q-number transform） in phase space quantum mechanics,∫∫∞-∞dp＇dq＇/π △（q＇,p＇）e-2i（ p-p＇）（ q-q＇）=δ（ p-P）δ（ q-Q）,∫∫∞-∞dqdpδ（p-P）δ（q-Q）e2i（p-p＇）（q-q＇）=△（q＇,p＇）,whereQ,P are the coordinate and momentum operators, respectively. We apply it to study mutual converting formulae among Q-P ordering, P-Q ordering and Weyl ordering of operators. In this way, the contents of phase space quantum mechanics can be enriched. The formula of the Weyl ordering of operators expansion and the technique of integration within the Weyl ordered product of operators are used in this discussion.

A Note on the Operator Equation Generalizing the Notion of Slant Hankel Operators

The operator equation λMz^-X = XMzk, for k ≥ 2,λ∈ C, is completely solved. Further, some algebraic and spectral properties of the solutions of the equation are discussed.

Mutual transformations between the P–Q, Q–P, and generalized Weyl ordering of operators

Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （p, q） with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （p, q）, which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.

YANG-BAXTER OPERATORS AND TENSOR TRANSFORMATIONS

The author considers relations between Yang-Baxter operators and tensor transformations, and proves that all tensor transform at ions over the category of modules of a Yang-space form a group.

Little Hankel Operators on the Weighted Bergman Space of the Unit Ball

In this paper we mainly consider little Hankel operators with squareintegrable symbols on the weighted Bergman spaces of the unit ball.We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that SMO（f） ∈ L p/2 （B n,dλ） and 2 ≤ p ∞,which is very important to research the relation between Toeplitz operators and little Hankel operators.

Coherent State Projection Operator Representation of Symplectic Transformations as a Loyal Representation of Symplectic Group

We find that the coherent state projection operator representation of symplectic transformation constitutesa loyal group representation of symplectic group. The result of successively applying squeezing operators on numberstate can be easily derived.

The Fourier slice transformation of the Wigner operator and the quantum tomogram of the density operator

Using the Weyl quantization scheme and based on the Fourier slice transformation （FST） of the Wigner operator, we construct a new expansion formula of the density operator p, with the expansion coefficient being the FST of p＇s classical Weyl correspondence, and the latter the Fourier transformation of p＇s quantum tomogram. The coordinate momentum intermediate representation is used as the Radon transformation of the Wigner operator.

New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

As a natural and important extension of Fan＇s paper （Fan Hong-Yi 2010 Chin. Phys. B 19 040305） by employing the formula of operators＇ Weyl ordering expansion and the bipartite entangled state representation this paper finds a new two-fold complex integration transformation about the Wigner operator A （#, ~） （in its entangled form） in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to （a1-a2） and （a1＋a2） can be solved and the contents of phase space quantum mechanics can be enriched, where ai,ai are bosonic creation and annihilation operators, respectively.

Cultivating New Agricultural Operators to Promote the Transformation and Upgrading of Traditional Agriculture——A Case Study of Nanchong City

In order to provide reference for cultivating new agricultural operators to promote the transformation and upgrading of traditional agriculture,the main practices,achievements and problems of cultivating new agricultural operators to promote the transformation and upgrading of traditional agriculture in Nanchong City,Sichuan Province were analyzed firstly,and then some measures were proposed.

Study Hankel Transforms and Properties of Bessel Function via Entangled State Representation Transformation in Quantum Mechanics

In Phys. Lett. A 313 （2003） 343 we have found that the self-recipràcal Hankel transformation （HT） is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations＇ transformation in quantum mechanics.

Gauge Transformation and Constraint Induced Operator Ordering for Charged Rigid Planar Rotator in Uniform Magnetic Field

When the motion of a particle is constrained, excess terms exist using hermitian form of Cartesian momentum pi （i=1, 2,3） in usual kinetic energy （1/2/μ）∑ pi^2 , and the correct kinetic energy turns out to be （1/2μ） ∑1/ fipi f ipi, where fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions fi is given for a charged rigid planar rotator in the uniform magnetic field with different gauge chosen. Under different gauges, we have different sets of dummy factors. It means that these factors do not have direct observable effect.

A Generalized Hankel Transformation Derived by Parametrized Entangled State Representations

Using the parametrized entangled state representations we have found a generalized Hankel transformationwith the integral kernel being a combination of Bessel functions.This generalized Hankel transformation corresponds tothe appropriate quantum mechanical representation transformation.

Capacity Openness Boosts Digitization Transformation of Telecom Operators

With the emergence of digital transformation success stories,more and more enterprises are launching digital solutions to improve business efficiency or achieve optimal revenue growth.The traditional communication market tends to be saturated,and the digital transformation of telecom operators is imminent.This article combining the development trend of telecom operators’product business and the application situation of the pilot summarizes the innovative application categories that telecom operators continue to launch based on their own advantages and in response to the needs of the industry.This article focuses on the transformation of security capabilities in communication services,big data,Internet of Things,artificial intelligence,unified authentication and network information security,and deeply analyzes the business characteristics and application modes from the aspects of resource integration,open platform construction,new connection construction,and innovative business development.This article puts forward suggestions for the security development of telecom operators,and provides basic research content for the subsequent research on the innovative application of telecom operators’capability openness.

A Note on Generalized Aluthge Transformation for p-hyponormal and Log-hyponormal Operators

We shall give some results on generalized aluthge transformation for phyponormal and log-hyponormal operators. We shall also discuss the best possibility of these results.