In a number of papers the description of Carleson measures for Bergman spaces of analytic, harmonic or quasiregular functions were given. The asymptotic formulae for spectrum bands of a number of periodical problems were given in the case when the period tends to infinity. The motion of waves or quantum particles through a periodical waveguide with screens was studied.
Main publications:
Oleinik V. L., “Carleson measures on Bergman spaces for domains with nonsmooth boundary”, Operator Theory: Advances and Applications, 113 (2000), 269–277
Oleinik V. L., “Metod priblizheniya silnoi svyazi na lemniskate”, Zapiski nauchnykh seminarov POMI, 270, 2000, 258–276
Oleinik V. L., “Carleson measures and uniformly perfect sets”, Journal of Mathematical Sciences, 107:4 (2001), 4029–4037
Oleinik V. L., “Rekurrentnye sootnosheniya i raznostnye uravneniya”, Sorosovskii obrazovatelnyi zhurnal, 7:3 (2001), 114–120
Oleinik V. L., Sibirev N. V., “Description of low-frequency parts of spectrum of periodical waveguide with screens”, International Seminar “Day on Diffraction'2001”, Proceedings, St. Petersburg, 2001, 194–201
