论文标题
双色框架
Bicomplex frames
论文作者
论文摘要
主要目的是介绍所谓的双色（BC） - 帧，这是对经典框架的双色无限希尔伯特空间的特殊扩展。至关重要的结果是BC框架的表征是根据其基本成分的角度来表征，从而导致对BC框架的某些结果的概括。尽管扩展是自然的，但是许多经典框架满足的基本属性对BC框架没有有效，除非我们将自己限制在双色复杂的希尔伯特空间上。通过从经典框架理论提供的洞察力中受益，我们讨论了BC-Frame Operator和Weyl-Heisenberg BC-Frames的构建，并提供了一些适合BC-Frames的新的。
The main purpose is to introduce the so-called bicomplex (bc)-frames which is a special extension to bicomplex infinite Hilbert spaces of the classical frames. The crucial result is the characterization of bc-frames in terms of their idempotent components, giving rise to generalization of certain results to bc-frames. Although the extension is natural, many basic properties satisfied by classical frames do not remain valid for bc-frames, unless we restrict ourself to complex-valued Hilbert space on bicomplex numbers. By benefiting from insight provided by the classical frame theory, we discuss the construction of bc-frame operator and Weyl--Heisenberg bc-frames and we provide some new ones which are appropriate for bc-frames.
