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.     

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.     

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.     

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．     

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.     

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.     

量子金融的意义

金融市场中的风险资产的演化过程遵从某种统计规律。这种统计规律通常是采用经典概率理论来加以阐述的。最近, 作者提出了从量子力学的角度来探讨金融问题的设想［1］,［2］,［3］。其中, 作者不仅从量子力学的角度用Maxwell Boltzmann统计重新推导了著名的Cox Ross Rubinstein期权定价公式，而且还用量子力学中的Bose Einstein统计(不可分辨粒子模型)得到了一个新的期权定价公式。这表明在理论上存在着一套关于金融市场的和谐的“量子理论”——量子金融。本文从对冲的角度来阐述这种潜在理论的金融意义和可能的实际内涵。作者给出了对冲定价的量子方案，详细讨论了单期金融市场的量子对冲问题。最后，作者解释了为什么（某些）金融市场在物理上要遵循量子规律，而不是经典统计规律。     

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。