q-变形量子空间上的量子运动学I，数学框架
Quantum kinematics on q-deformed quantum spaces I, Mathematical Framework
摘要：
这两篇论文（I和II）的目的是试图给出q变形量子空间的量子运动学的基本概念。论文一介绍了相关的数学概念。简要回顾了q变形分析的基本思想。通过引入傅立叶变换和δ函数的q变形类似物来继续这些考虑。详细讨论了它们的性质。此外，q-变形版本的sesquilinear形式的定义，其基本性质的推导，并证明了q-类似的Fourier-Plancherel身份。在论文II中，这些推论被应用于位置和动量空间上的波函数。
英文摘要：
The aim of these two papers (I and II) is to try to give fundamental concepts of quantum kinematics to q-deformed quantum spaces. Paper I introduces the relevant mathematical concepts. A short review of the basic ideas of q-deformed analysis is given. These considerations are continued by introducing q-deformed analogs of Fourier transformations and delta functions. Their properties are discussed in detail. Furthermore, q-deformed versions of sesquilinear forms are defined, their basic properties are derived, and q-analogs of the Fourier-Plancherel identity are proved. In paper II these reasonings are applied to wave functions on position and momentum space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
