Open AccessDirect and Inverse Problems of Spectral Analysis for Arbitrary-Order Differential Operators with Nonintegrable Regular Singularities
Author(s) -
V. A. Yurko
Publication year - 2021
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2021-67-2-408-421
Subject(s) - mathematics , gravitational singularity , completeness (order theory) , differential operator , integrable system , inverse , order (exchange) , spectral theorem , spectral theory , mathematical analysis , class (philosophy) , microlocal analysis , pure mathematics , differential (mechanical device) , operator theory , fourier integral operator , geometry , physics , computer science , finance , hilbert space , artificial intelligence , economics , thermodynamics
A short review is presented of results on the spectral theory of arbitrary order ordinary differential operators with non-integrable regular singularities. We establish properties of spectral characteristics, prove theorems on completeness of root functions in the corresponding spaces, prove expansion and equiconvergence theorems, and provide a solution of the inverse spectral problem for this class of operators.