标题： 一维狄拉克算子在常规边界条件下的谱分解的等收敛性 显示英文标题

标题： Equiconvergence of spectral decompositions of 1D Dirac operators with regular boundary conditions

摘要： 一维狄拉克算子$$ L_{bc}(v) y = i 1 & 0 0 & -1 \frac{dy}{dx} + v(x) y, \quad y = y_1 y_2, \quad x\in[0,\pi]$$，考虑带有$L^2$-势$ v(x) = 0 & P(x) Q(x) & 0$并满足正则边界条件（$bc$）时，具有离散谱。对于严格正则的$bc,$，自由算子$ L_{bc}(0) $的谱是简单的，而$ L_{bc}(v) $的谱最终是简单的，相应的归一化根函数系是里斯基。 对于这些Riesz基附近有界变分函数的展开，我们证明了均匀等收敛性和闭区间$[0,\pi].$上的逐点收敛性。对于正则但不严格正则的$bc.$也得到了类似的结果。 显示英文摘要

摘要： One dimensional Dirac operators $$ L_{bc}(v) y = i 1 & 0 0 & -1 \frac{dy}{dx} + v(x) y, \quad y = y_1 y_2, \quad x\in[0,\pi]$$, considered with $L^2$-potentials $ v(x) = 0 & P(x) Q(x) & 0$ and subject to regular boundary conditions ($bc$), have discrete spectrum. For strictly regular $bc,$ the spectrum of the free operator $ L_{bc}(0) $ is simple while the spectrum of $ L_{bc}(v) $ is eventually simple, and the corresponding normalized root function systems are Riesz bases. For expansions of functions of bounded variation about these Riesz bases, we prove the uniform equiconvergence property and point-wise convergence on the closed interval $[0,\pi].$ Analogous results are obtained for regular but not strictly regular $bc.$