Analytic Hardy spaces on the quantum torus

Analytic Hardy and BMO spaces on the quantum torus are introduced. Some basic properties of these spaces are presented. In particular, the associated H 1-BMO duality theorem is proved. Finally, we discuss some possible extensions of the obtained results.     

GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION

A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators dt and its dual, creation operators t*.     

Concurrence and Wigner-Yanase Skew Information

A measure of entanglement on n qubits is defined in terms of Wigner-Yanase skew information. It is shown that the measure coincides essentially with the concurrence on two qubits. This uncovers the information-theoretic meaning of the concurrence of entangled states.     

Gross-Pitaevskii级联的局部适定性

研究Gross-Pitaevskii无穷线性级联的Cauchy问题.通过在密度矩阵序列的Sobolev型空间中引进一个(F)-范数,我们建立了解的局部存在性,唯一性和稳定性;也得到了解的明显空时估计.特别是,当初始值为分离形式时这个(F)-范数与通常的Sobolev范数是一致的.     

AREA INTEGRAL FUNCTIONS AND H∞ FUNCTIONAL CALCULUS FOR SECTORIAL OPERATORS ON HILBERT SPACES

Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.     

无限状态空间上的Radon-Nikodym性质(I)

利用有界变差向量测度空间给出一个Ｂａｎａｃｈ空间有Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性质的内蕴几何刻划，所用工具为本文引进的向量测度值鞅．     

Bochner积分的推广

引进偏Bochner积分的概念．证明了在不可分清形下,偏Bochner积分与Bochner积分有本质的差异．作为应用,通过向量测度空间用价Bochner积分给出了Radon－Nikodym性质的一个刻划．     

AREA INTEGRAL FUNCTIONS FOR SECTORIAL OPERATORS ON L^p SPACES

Area integral functions are introduced for sectorial operators on Lp-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on Lpspaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H∞functional calculus of sectorial operators on Lp-spaces hold true when the square functions are replaced by the area integral functions.     

参数化测度与一类算子的表示问题

本文利用参数化测试研究一类算子的表示问题，得到了所谓的参数化的Ｒｉｅｚｅ表示定理。     

加权解析Lipschitz空间的等价范数

该文研究单位圆盘上加权解析Lipschitz空间的等价范数。作者首先推广文献［3］中的结果，给出了加权解析Lipschitz函数的p Garsia模刻画，然后用高阶导数刻画了加权解 析Lipschitz函数，并给出了它的Bergman Carleson测度特征。最后，还得到了加权解析Lipschitz函数类似于BMO指数衰减的John Nirenberg定理。