Generalized Fock space and moments

Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales

The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence of generalized functional sequences of a discrete-time normal martingale $M$. A necessary and sufficient condition in terms of the Fock transform is obtained for such a sequence to be strong convergent. A type of generalized martingales associated with $M$ are introduced and their convergence theorems are established. Some applications are also shown.

分离行列式点过程与广义Fock空间

Separated determinantal point processes and generalized Fock spaces

本文刻画了由倍增次调和权定义的广义Fock空间所对应行列式点过程几乎必然分离的条件，并通过与同强度Poisson过程比较揭示内在排斥力的作用，证明典范权情形下分离的临界指数为α<4/3。

(q,2)-Fock空间的概率分析：真空态分布与场算子的矩

Probabilistic Analysis of the (q,2)-Fock Space: Vacuum Distribution and Moments of the Field Operator

本文主要研究(q,2)-Fock空间上关键算子关于重要状态的分布，重点分析了场算子的真空态分布。

Identification of the theory of multidimensional orthogonal polynomials with the theory of symmetric interacting Fock spaces with finite dimensional one particle space

The identification mentioned in the title allows a formulation of the multidi mensional Favard Lemma different from the ones currently used in the literature and which exactly parallels the original one dimensional formulation in the sense that the positive Jacobi sequence is replaced by a sequence of positive Hermitean (square) matrices and the real Jacobi sequence by a sequence of Hermitean matri ces of the same dimension. Moreover, in this identification, the multidimensional extension of the compatibility condition for the positive Jacobi sequence becomes the condition which guarantees the…