G. M. Vodinchar, L. K. Feshchenko, “Orthogonal solutions of a spectral problem in the class of poloidal field”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2011, Number 1(2),Pages <nobr>26

MATHEMATICS

Orthogonal solutions of a spectral problem in the class of poloidal field

G. M. Vodinchar^ab, L. K. Feshchenko^a

^a Institute of Cosmophysical Researches and Radio Wave Propagation Far-Eastern Branch Russian Academy of Sciences, 684034, Kamchatskiy Kray, Paratunka, Mirnaya st., 7, Russia
^b Kamchatka State University by Vitus Bering, 683032, Petropavlovsk-Kamchatsky, Pogranichnaya st., 4, Russia

Abstract: We prove the orthogonality of the eigenfields of the spectral problem $\mathrm{rot}\Delta S+\lambda \mathrm{rot}S =0$ in the space of the poloidal field in a spherical shell.

Keywords: spectral problem; the spherical shell; orthogonal field.

UDC: 517.958+517.927

MSC: Primary 47F05; Secondary 57R25

Received: 05.02.2011

DOI: 10.18454/2079-6641-2011-2-1-24-29