零点渐近分离的恢复正弦型函数的一致稳定性
On the uniform stability of recovering sine-type functions with asymptotically separated zeros
摘要：
我们得到了从零点恢复一种特殊形式整函数的一致稳定性。对于这种形式，人们可以将强正则微分算子和一阶和二阶束的特征行列式约化，包括具有渐近分离特征值的微分系统，其示性数位于包含原点的直线上，以及它们的非局部扰动。我们建立了这样的函数对它们的零点序列的依赖性具有Lipschitz性质，关于每个有限半径的球上的自然度量。这类结果可用于研究谱反问题的一致稳定性。此外，还得到了这类函数零点的渐近性及其通过无穷乘积的等价表示的一般定理，并对许多特殊算子给出了相应的结果.
英文摘要：
We obtain a uniform stability of recovering entire functions of a special form from their zeros. To this form, one can reduce the characteristic determinants of strongly regular differential operators and pencils of the first and the second orders, including differential systems with asymptotically separated eigenvalues whose characteristic numbers lie on a line containing the origin, and their non-local perturbations. We establish that the dependence of such functions on the sequences of their zeros possesses the Lipschitz property with respect to natural metrics on each ball of a finite radius. Results of this type can be used for studying the uniform stability of inverse spectral problems. In addition, general theorems on the asymptotics of zeros of functions of this class and on their equivalent representation via an infinite product are obtained, which give the corresponding results for many specific operators.
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