Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
16.07.1943
E-mail: ,
Website: https://www.imm.uran.ru Keywords: approximation of functions; extremal properties of polynomials and entire functions; harmonic analysis; positive definite functions; approximation of operators; ill-posed problems.
Subject:
The problem of the best approximation of unbounded operators by bounded ones was studied. Some mutual relation was established between this problem and the problem of the least constants in inequalities between norms of derivatives of differentiable functions (Kolmogorov inequalities), the problem of the best approximation of one class of functions by another class of more smooth functions, the ill-posed problem of optimal recovery of unbounded operators on classes of elements given with an error. Solution of these problems was found in a number of concrete cases. It was created a method of investigation of problems for trigonometric polynomials in the spaces $L_p, 0\le p<1$; the best constant in Bernstein inequality for trigonometric polynomials in $L_p, 0\le p<1$ was found with the help of this method. Cojointly with A. G. Babenko it was solved Delsarte problem which is connected with the problem about contact number of four-dimensional Euclidian space.
Main publications:
Arestov V. V. Ob integralnykh neravenstvakh dlya trigonometricheskikh polinomov i ikh proizvodnykh // Izv. AN SSSR. Ser. matem. 1981. T. 45, # 1. S. 3–22.
Arestov V. V. Integralnye neravenstva dlya algebraicheskikh mnogochlenov na edinichnoi okruzhnosti // Matem. zametki. 1990. T. 48, vyp. 4. S. 7–18.
Arestov V. V. Priblizhenie neogranichennykh operatorov ogranichennymi i rodstvennye ekstremalnye zadachi // Uspekhi matem. nauk. 1996. T. 51, vyp. 6. S. 89–124.
Arestov V. V., Babenko A. G. O skheme Delsarta otsenki kontaktnykh chisel // Trudy Matem. in-ta im. V. A. Steklova RAN. 1997. T. 219: Teoriya priblizhenii. Garmonicheskii analiz. S. 44–73.
Arestov V. V. Nailuchshee priblizhenie odnogo klassa funktsii mnogikh peremennykh drugim i rodstvennye ekstremalnye zadachi // Matem. zametki. 1998. T. 64, vyp. 3. S. 323–340.
