奇异Sturm-Liouville方程的正则化
Regularization of singular Sturm-Liouville equations
摘要：
本文研究了有限区间上的奇异Sturm-Liouville表达式$$l(y) = -(py')' + qy$$，其中函数$Q$的导数是在分布的意义下理解的，其系数为$$q = Q', \quad 1/p, Q/p, Q^2/p \in L_1,$$.由于一个新的正则化相应的运营商被正确地定义为拟微分。研究了它们的预解式近似，并将所有的自伴和最大耗散扩张以及广义预解式用正则形式的齐次边界条件描述。有些结果对于$p(t)\equiv 1$情形也是新的。
英文摘要：
Paper deals with the singular Sturm-Liouville expressions $$l(y) = -(py')' + qy$$ on a finite interval with coefficients $$q = Q', \quad 1/p, Q/p, Q^2/p \in L_1,$$ where derivative of the function $Q$ is understood in the sense of distributions. Due to a new regularization corresponding operators are correctly defined as quasi-differential. Their resolvent approximation is investigated and all self-adjoint and maximal dissipative extensions and generalized resolvents are described in terms of homogeneous boundary conditions of the canonic form. Some results are new for the case $p(t)\equiv 1$ as well.
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。
