Investigation of One Linear Differential Equation by Using Generalized Functions with Values in a Banach Space

  • A. V. Chaikovs'kyi Київ. нац. ун-т iм. Т. Шевченка

Abstract

We present a generalization of some facts of the theory of generalized functions of slow growth to the case of operator-valued test functions. We propose a construction of regular generalized functions with values in a Banach space. The results obtained are used for the description of slowly increasing solutions of linear homogeneous differential equations with shifted arguments and bounded operator coefficients in a Banach space.
Published
25.05.2001
How to Cite
Chaikovs’kyiA. V. “Investigation of One Linear Differential Equation by Using Generalized Functions With Values in a Banach Space”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 5, May 2001, pp. 688-93, https://umj.imath.kiev.ua/index.php/umj/article/view/4290.
Section
Research articles