q-线性网格上的完备性、特殊函数和测不准原理
Completeness, special functions and uncertainty principles over q-linear grids
摘要：
我们推导出完整性准则序列的形式$% f(xλ_{n})$，其中$λ_{n}$是$nth$零的适当选择的整个功能。利用这些准则，我们构造了非正交的Fourier-Bessel函数系统及其$q$ -类似物，以及其他$q$ -特殊函数的完备集。然后利用$q$ -Bessel函数的完备性证明了：如果函数$f$及其$q$ -Hankel变换在点$\{q^{-n}\}_{n=1}^{% \infty}$，$0<q<1$处均为零，则$f$在整个$q$ -线性网格$% \{q^{n}\} _{n=-\infty}^{\infty}$上必为零.
英文摘要：
We derive completeness criteria for sequences of functions of the form $% f(xλ_{n})$, where $λ_{n}$ is the $nth$ zero of a suitably chosen entire function. Using these criteria, we construct systems of nonorthogonal Fourier-Bessel functions and their $q$-analogues, as well as other complete sets of $q$-special functions. The completeness of certain sets of $q$-Bessel functions is then used to prove that, if a function $f$ and its $q$-Hankel transform both vanish at the points $\{q^{-n}\}_{n=1}^{% \infty}$, $0<q<1$, then $f$ must vanish on the whole $q$-linear grid $% \{q^{n}\} _{n=-\infty}^{\infty}$.
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。
