论文标题
福克空间上的换向器
Commutators on Fock spaces
论文作者
论文摘要
给定加权$ \ ell^2 $空间，具有与整个功能相关的权重，我们考虑了一对加权转移操作员，当将其视为一般FOCK空间的操作员时，其换向器是对角线运算符。我们为这些换向器的代数建立了一个演算，并将其应用于Gelfond-Leontiev衍生物的一般情况。这类操作员类别包括许多已知的示例，例如经典的分数衍生物和dunkl操作员。这使我们能够建立一个超越经典的Weyl-Heisenberg代数的通用框架。提供了其应用的具体示例。
Given a weighted $\ell^2$ space with weights associated to an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a calculus for the algebra of these commutators and apply it to the general case of Gelfond-Leontiev derivatives. This general class of operators includes many known examples, like classic fractional derivatives and Dunkl operators. This allows us to establish a general framework which goes beyond the classic Weyl-Heisenberg algebra. Concrete examples for its application are provided.
