2022/07/10 by Kukushkin, Maksim V.
#34K30 #47A10 #47B10 #47B12 #47B28 #58D25 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2207.04392
In this paper, having introduced a convergence of a series on the root vectors in the Abel-Lidskii sense, we present a valuable application to the evolution equations. The main issue of the paper is an approach allowing us to principally broaden conditions imposed upon the right-hand side of the evolution equation in the abstract Hilbert space. In this way, we come to the definition of the function of an unbounded non-selfadjoint operator. Meanwhile, considering the main issue we involve an additional concept that is a generalization of the spectral theorem for a non-selfadjoint operator.