Abstract:
We describe the spectrum of a difference operator (a weighted shift operator). We obtain applications to finding spectra of differential operators in weighted function spaces.
Keywords:
difference operator, differential operator, operator spectrum, weighted spaces of sequences and functions.
Citation:
M. S. Bichegkuev, S. V. Besaeva, “Spectral properties of difference and differential operators in weighted spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 2, 16–21; Russian Math. (Iz. VUZ), 55:2 (2011), 13–17
This publication is cited in the following 6 articles:
A. G. Baskakov, G. V. Garkavenko, N. B. Uskova, L. N. Kostina, “Ob ekvivalentnykh operatorakh”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXV», Voronezh, 26-30 aprelya 2024 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 235, VINITI RAN, M., 2024, 3–14
N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405
S. V. Besaeva, “On the spectra of difference relations and differential operators on weighted spaces of sequences and functions”, St. Petersburg Math. J., 26:4 (2015), 499–513
A. G. Baskakov, “Analysis of linear differential equations by methods of the spectral theory of difference operators and linear relations”, Russian Math. Surveys, 68:1 (2013), 69–116
M. S. Bichegkuev, “Spectral analysis of difference and differential operators in weighted spaces”, Sb. Math., 204:11 (2013), 1549–1564
Besaeva S.V., “O spektre raznostnykh operatorov v vesovykh prostranstvakh”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2011, no. 1, 94–99