An analog of the rolle theorem for differential operators and $L$-spline interpolation

• Date: 1993
• Main Authors: Novikov, S. I., Новиков, С. И.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5909
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

An analog of the Rolle theorem is established for linear differential operators with continuous periodic coefficients. By using this result, exact values of the deviations of interpolational $L$-splines are obtained on certain classes of functions given by a linear differential operator.