论文标题
普遍加权数量运算符在离散时间正常martingales的功能上
Generalized weighted number operators on functionals of discrete-time normal martingales
论文作者
论文摘要
让$ m $成为具有混乱代表属性的离散时间普通玛格尔。然后，从$ M $的Square Antekable功能的空间中，可以构建$ M $的广义功能。在本文中，通过使用一种权重，我们引入了一类连续的线性运算符，这些连续性运算符作用于$ M $的广义功能，我们称之为广义加权号码（GWN）运算符。我们证明，GWN运营商可以用广义的歼灭和创建操作员表示（作用于$ M $的广义功能）。我们还研究了GWN操作员与广义歼灭（或创建）操作员之间的换向关系，并获得了表达这种换向关系的几个公式。
Let $M$ be a discrete-time normal martingale that has the chaotic representation property. Then, from the space of square integrable functionals of $M$, one can construct generalized functionals of $M$. In this paper, by using a type of weights, we introduce a class of continuous linear operators acting on generalized functionals of $M$, which we call generalized weighted number (GWN) operators. We prove that GWN operators can be represented in terms of generalized annihilation and creation operators (acting on generalized functionals of $M$). We also examine commutation relations between a GWN operator and a generalized annihilation (or creation) operator, and obtain several formulas expressing such commutation relations.
