The relation between composition operators on the Dirichlet spaces in the open unit disk and derivative weighted composition operators on the Bergman spaces in the open unit disk is investigated firstly,and for a comb...The relation between composition operators on the Dirichlet spaces in the open unit disk and derivative weighted composition operators on the Bergman spaces in the open unit disk is investigated firstly,and for a combination of several derivative weighted composition operators which acts on classic Bergman space,the lower bound of its essential norm is estimated in terms of the boundary data of the symbols of d-composition operators.Some similar results about composition operators on the Dirichlet space are also presented.A necessary condition is given to determine the compactness of the combination of several derivative weighted composition operators on Bergman spaces.展开更多
We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic ■ and ψ, S■Sψ= SψS■ on(L2h)⊥if and only if ■...We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic ■ and ψ, S■Sψ= SψS■ on(L2h)⊥if and only if ■ and ψ satisfy one of the following conditions:(1) Both ■ and ψ are analytic on D.(2) Both ■ and ψ are anti-analytic on D.(3) There exist complex constants α and β, not both 0, such that ■ = αψ + β.Furthermore, we give the necessary and sufficient conditions for S■Sψ= S■ψ.展开更多
The authors express the essential norms of composition operators between Hardy spaces of the unit disc in terms of the natural Nevanlinna counting function.
Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator Cφ: Cφf = f °φ, for all f ∈ X. In this paper, the boundedness and ...Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator Cφ: Cφf = f °φ, for all f ∈ X. In this paper, the boundedness and compactness of the composition operators from α-Bloch spaces into QK(p,q) and QK,0(p,q) spaces are discussed, where 0 < α < ∞.展开更多
The so-called blisks,i.e.integrally bladed disks,are characterized by very low viscous material damping and make the flutter prediction much more critical.In that framework,a two-dimensional numerical study of a space...The so-called blisks,i.e.integrally bladed disks,are characterized by very low viscous material damping and make the flutter prediction much more critical.In that framework,a two-dimensional numerical study of a space turbine blisk featuring complex deformation of blades and high eigenfrequency(>40kHz)is performed.The simulations are based on unsteady Reynolds Averaged Navier Stokes computations linearized in the frequency domain and consist in the superposition of an unsteady linear(in time)pressure field,generated by a harmonic perturbation,upon a steady nonlinear(in space)flow.The aerodynamic damping coefficient is calculated over a range of nodal diameters,and the blades are predicted aeroelastically stable.However,violent changes occur and are rather critical since sudden and large deviations in stability appear.In that context,the nature of the waves propagating from the cascade are evaluated.Such an approach provides fundamental knowledge about the perturbations which can either propagate to the far-field(cut-on mode)or decay(cut-off mode).It is expected that the ability of the flow to damp or to amplify the blade motion is strongly affected by the way unsteady perturbations are transferred from the cascade to the far-field.The nature of the waves are first assessed from the aforementioned linearized results,then they are evaluated analytically and finally compared.A good agreement is found despite the strong assumptions of the analytical model.The results show a clear correlation between the cut-on/cut-off conditions and stability.The least stable configuration corresponds to cut-off mode at the inlet and no wave at the outlet.Without outgoing waves from the cascade,the blade is prone to be less stable:the energy from the blades vibration is necessarily dissipated or sent out by the cascade.展开更多
基金Supported by National Natural Science Foundation of China (No. 10971153 and No. 10671141)
文摘The relation between composition operators on the Dirichlet spaces in the open unit disk and derivative weighted composition operators on the Bergman spaces in the open unit disk is investigated firstly,and for a combination of several derivative weighted composition operators which acts on classic Bergman space,the lower bound of its essential norm is estimated in terms of the boundary data of the symbols of d-composition operators.Some similar results about composition operators on the Dirichlet space are also presented.A necessary condition is given to determine the compactness of the combination of several derivative weighted composition operators on Bergman spaces.
基金supported by National Natural Science Foundation of China(Grant Nos.10971020 and 1127059)Research Fund for the Doctoral Program of Higher Education of China
文摘We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic ■ and ψ, S■Sψ= SψS■ on(L2h)⊥if and only if ■ and ψ satisfy one of the following conditions:(1) Both ■ and ψ are analytic on D.(2) Both ■ and ψ are anti-analytic on D.(3) There exist complex constants α and β, not both 0, such that ■ = αψ + β.Furthermore, we give the necessary and sufficient conditions for S■Sψ= S■ψ.
基金Project supported by the National Natural Science Foundation of China (No. 10771201)the Anhui Provincial Natural Science Foundation of China (No. 090416233)
文摘The authors express the essential norms of composition operators between Hardy spaces of the unit disc in terms of the natural Nevanlinna counting function.
基金the National Natural Science Foundation of China (No.10471039)the Grant of Higher Schools’ Natural Science Basic Research of Jiangsu Province of China (Nos.06KJD110175 07KJB110115)
文摘Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator Cφ: Cφf = f °φ, for all f ∈ X. In this paper, the boundedness and compactness of the composition operators from α-Bloch spaces into QK(p,q) and QK,0(p,q) spaces are discussed, where 0 < α < ∞.
基金the Centre National d'Etudes Spatiales (CNES) and Snecma for their financial supportthe Centre Informatique National de l'Enseignement Supérieur (CINES) for the computational resources,and the Agence Nationale de la Recherche(ANR) for sponsoring the project ANR-08-2009 CapCAO (parametrization-aided optimized aeroelastic design)
文摘The so-called blisks,i.e.integrally bladed disks,are characterized by very low viscous material damping and make the flutter prediction much more critical.In that framework,a two-dimensional numerical study of a space turbine blisk featuring complex deformation of blades and high eigenfrequency(>40kHz)is performed.The simulations are based on unsteady Reynolds Averaged Navier Stokes computations linearized in the frequency domain and consist in the superposition of an unsteady linear(in time)pressure field,generated by a harmonic perturbation,upon a steady nonlinear(in space)flow.The aerodynamic damping coefficient is calculated over a range of nodal diameters,and the blades are predicted aeroelastically stable.However,violent changes occur and are rather critical since sudden and large deviations in stability appear.In that context,the nature of the waves propagating from the cascade are evaluated.Such an approach provides fundamental knowledge about the perturbations which can either propagate to the far-field(cut-on mode)or decay(cut-off mode).It is expected that the ability of the flow to damp or to amplify the blade motion is strongly affected by the way unsteady perturbations are transferred from the cascade to the far-field.The nature of the waves are first assessed from the aforementioned linearized results,then they are evaluated analytically and finally compared.A good agreement is found despite the strong assumptions of the analytical model.The results show a clear correlation between the cut-on/cut-off conditions and stability.The least stable configuration corresponds to cut-off mode at the inlet and no wave at the outlet.Without outgoing waves from the cascade,the blade is prone to be less stable:the energy from the blades vibration is necessarily dissipated or sent out by the cascade.