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.
Biography
Graduated from Physical Faculty of Leningrad State University (LSU) in 1967 (department of higher mathematics and mathematical physics). Ph.D. thesis was defended in 1975. A list of my scientific works contains more than 50 titles.
In 1993 I won a Soros scholarship of Russian Academy of Natural Sciences and International Science Foundation. Soros associate professor 1997, 1998, and 1999.
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
V. L. Oleinik, B. S. Pavlov, “Embedded spectrum on a metric graph (an observation)”, Zap. Nauchn. Sem. POMI, 300 (2003), 215–220; J. Math. Sci. (N. Y.), 128:2 (2005), 2803–2806
A. P. Kalupin, V. L. Oleinik, “A lemniscate as the spectrum of a perturbed shift”, Zap. Nauchn. Sem. POMI, 282 (2001), 74–91; J. Math. Sci. (N. Y.), 120:5 (2004), 1685–1695
2000
3.
V. L. Oleinik, “Tight-binding approximation on the lemniscate”, Zap. Nauchn. Sem. POMI, 270 (2000), 258–276; J. Math. Sci. (N. Y.), 115:2 (2003), 2233–2242
1998
4.
V. L. Oleinik, “Carleson measures and uniformly perfect sets”, Zap. Nauchn. Sem. POMI, 255 (1998), 92–103; J. Math. Sci. (New York), 107:4 (2001), 4029–4037
A. L. Mironov, V. L. Oleinik, “Limits of applicability of the tight binding approximation for complex-valued potential function”, TMF, 112:3 (1997), 448–466; Theoret. and Math. Phys., 112:3 (1997), 1157–1171
V. L. Oleinik, “Carleson measures and the heat equation”, Zap. Nauchn. Sem. POMI, 247 (1997), 146–155; J. Math. Sci. (New York), 101:3 (2000), 3133–3138
V. N. Kudashov, V. L. Oleinik, “Theorems on the Embedding of Bergman Spaces in Lebesgue Spaces for Domains with Nonsmooth Boundary”, Funktsional. Anal. i Prilozhen., 30:1 (1996), 67–70; Funct. Anal. Appl., 30:1 (1996), 52–54
G. V. Galunov, V. L. Oleinik, “Exact inequalities for norms of intermediate derivatives of quasiperiodic functions”, Mat. Zametki, 56:6 (1994), 127–130; Math. Notes, 56:6 (1994), 1300–1303
A. L. Mironov, V. L. Oleinik, “Limits of applicability of the tight binding approximation”, TMF, 99:1 (1994), 103–120; Theoret. and Math. Phys., 99:1 (1994), 457–469
G. V. Galunov, V. L. Oleinik, “Analysis of the dispersion equation for a negative Dirac “comb””, Algebra i Analiz, 4:4 (1992), 94–109; St. Petersburg Math. J., 4:4 (1993), 707–720
V. L. Oleinik, G. S. Perel'man, “Carleson's imbedding theorem for a weighted Bergman space”, Mat. Zametki, 47:6 (1990), 74–79; Math. Notes, 47:6 (1990), 577–581
V. L. Oleinik, “Estimates for the $n$-widths of compact sets of differentiate functions in spaces with weight functions”, Zap. Nauchn. Sem. LOMI, 59 (1976), 117–132; J. Soviet Math., 10:2 (1978), 286–298
1974
13.
V. L. Oleinik, “Embedding theorems for weighted classes of harmonic and analytic functions”, Zap. Nauchn. Sem. LOMI, 47 (1974), 120–137
1971
14.
V. L. Oleinik, B. S. Pavlov, “Embedding theorems for the weighted class of harmonic and analytic functions”, Zap. Nauchn. Sem. LOMI, 22 (1971), 94–102
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