2024/01/11 by Maksim V. Kukushkin, Kukushkin, Maksim V.
Mathematics · #34K30 #47A10 #47B10 #47B12 #47B28 #58D25 #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Iterative Methods for Nonlinear Equations
paper · pdf · doi:10.48550/arxiv.2402.03331
openalex publication_date 2024/01/11 · openalex created_date 2024/02/09 · openalex updated_date 2026/07/28
In this monograph, we formulated the sufficient conditions of the Abel-Lidskii basis property for a sectorial operator. Having studied such an operator class, we strengthened the conditions regarding the semi-angle of the sector and weakened a great deal conditions regarding the involved parameters. Thus, we clarified the results by Lidskii V.B. devoted to the decomposition on the root vector system of the non-selfadjoint operator. We used a technique of the entire function theory and introduced the so-called Schatten-von Neumann class of the convergence exponent. Having considered strictly accretive operators satisfying special conditions formulated in terms of the norm and used a sequence of contours of the power type, we invented a peculiar method how to calculate a contour integral involved in the problem. Finally, we consider evolution equations in the abstract Hilbert space.