In the present article, we compute the spectra of the generalized difference operator \(B_\nu ^{(m)}\) over the sequence space \(c_0\). In fact, the difference operator \(B_\nu ^{(m)}\) usually generalizes several difference operators such as first-order difference operators (\(\Delta _{ab}, B(r,s),\Delta\) and \(\Delta _\nu\)), second-order difference operators (\(\Delta ^2, B(r,s,t)\) and \(\Delta _{uv}^2\)), third-order difference operator(B(r, s, t, u)), difference operators \((\Delta ^m\) and \(\Delta _\nu ^m)\) of order \(m\in {\mathbb{N}}\) and many others. Therefore, the results obtained are more general and interesting than those derived earlier.

中文翻译：

---

关于广义差分算子及其精细谱

在本文中，我们计算了序列空间\（c_0 \）上的广义差分算子\（B_ \ nu ^ {（m）} \）的谱。实际上，差分算子\（B_ \ nu ^ {{（m）} \\）通常归纳一些差分算子，例如一阶差分算子（\（\ Delta _ {ab}，B（r，s），\ Delta \）和\（\ Delta _ \ nu \）），二阶差分运算符（\（\ Delta ^ 2，B（r，s，t）\）和\（\ Delta _ {uv} ^ 2 \）），三阶差分算子（B（r，  s，  t，  u）），差分算子\（（\ Delta ^ m \）和\（\德尔塔_ \ NU ^ M）\）的顺序在{\ mathbb {N}} \）\（M \和许多其他。因此，所获得的结果比以前得出的结果更为笼统和有趣。