论文标题
$ p-adic $ hermite操作员的光谱理论
Spectral theory of $p-adic$ Hermite operator
论文作者
论文摘要
我们给出了$ p-adic $ hermite运营商的定义，并设置了$ p-adic $频谱措施。我们将Archimedean案件与非Archimedean案进行比较。 Hermite共轭在$ C^{*} $ - 代数中的结构对应于三个规范结构的$ P-ADIC $ $ PADIC $ ULTRAMETRECRIC BANACH代数：1。Mod$ p $降低2。FrobeniusMap3。TeichmüllerLift。 Galois理论与Hermite操作员光谱分解之间存在自然联系。 GALOIS组$ \ MATHRM {gal}（\ bar {\ Mathbb {f}} _ P | \ Mathbb {f} _p）$生成$ padic $频谱度量。我们指出了与$ padic $ $量子力学的一些关系：1。创建操作员和歼灭操作员2。$ p-adic $不确定性原理。
We give the definition of $p-adic$ Hermite operator and set up the $p-adic$ spectral measure. We compare the Archimedean case with non-Archimedean case. The structure of Hermite conjugate in $C^{*}$-Algebra corresponds to three canonical structures of $p-adic$ ultrametric Banach algebra: 1. mod $p$ reduction 2. Frobenius map 3. Teichmüller lift. There is a nature connection between Galois theory and Hermite operator spectral decomposition. The Galois group $\mathrm{Gal}(\bar{\mathbb{F}}_p|\mathbb{F}_p)$ generate the $p-adic$ spectral measure. We point out some relationships with $p-adic$ quantum mechanics: 1. creation operator and annihilation operator 2. $p-adic$ uncertainty principle.
