On Maximal Regularity of Differential and Difference Operators
In this paper we investigate a linear degenerate second-order difference operator and we find conditions that are sufficient for its bounded invertibility and separability in Hilbert space. We apply these results to prove the solvability of an infinite quasilinear difference system. We also give one result on the separability of its continuous analogue (a degenerate differential operator of second order) and show that the second-order discrete operator is separable under much weaker conditions.
This research was supported by the grant AP05131649 of the Ministry of Education and Science of the Republic of Kazakhstan.
- 2.M.C. Wang, G.E. Uhlenbeck, Reviews of Modern Physics (American Physical Society, Minneapolis, 1945)Google Scholar
- 3.S.S. Voit, The propagation of initial condensation in a viscous gas. Uch. Zap. MGU. Mechanics 5, 125–142 (1954)Google Scholar
- 4.E.I. Shemyakin, The propagation of the time-dependent perturbation in a visco-elastic medium. Soviet Math. Dokl. I04(1), 34–37 (1955)Google Scholar
- 5.S.A. Gabov, A.G. Sweshnikov, The Problems of Dynamics of Stratified Fluids (Nauka, Moscow, 1986, in Russian)Google Scholar
- 6.A.N. Tikhonov, A.A. Samarskiy, Equations of Mathematical Physics (Macmillan, New York, 1963)Google Scholar
- 7.V.I. Bogachev, N.V. Krylov, M. Rockner, S.V. Shaposhnikov, Fokker–Planck–Kolmogorov Equations. Mathematical Surveys and Monographs, vol. 207 (American Mathematical Society, Providence, 2015)Google Scholar
- 8.M.A. Naimark, Linear Differential Equations (Nauka, Moscow, 1969, in Russian)Google Scholar
- 12.K.T. Mynbayev, M. Otelbaev, Weighted Function Spaces and Spectrum of the Differential Operators (Nauka, Moscow, 1988, in Russian)Google Scholar
- 16.K.N. Ospanov, On types of the resolvent of a complete second order differential operator. Am. Inst. Phys. Conf. Proc. 1676, 020071-1–020071-4 (2015)Google Scholar