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.
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Chaikovs'kyi, A.V. Investigation of One Linear Differential Equation by Using Generalized Functions with Values in a Banach Space. Ukrainian Mathematical Journal 53, 796–803 (2001). https://doi.org/10.1023/A:1012586502109
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DOI: https://doi.org/10.1023/A:1012586502109