A scheme of obtaining direct and indirect theorems of theory of approximation, invented by professor N. P. Kuptsov was shown to be used in spaces $C(-\infty,\infty)$, $C[0,\infty)$. A necessary and sufficient condition of Lagrange–Hermit interpolation process's convergence was obtained in case of uniformly weighted norm. It was pointed out that the left boundary of Mhaskar–Rahmanov–Saff inequality, connected with Laguerre weight, is not asymptotically precise. The way of receiving asymptotically true boundaries in the number of cases was shown.
Main publications:
O vybore uzlov interpolirovaniya v prostranstve $C(-\infty,\infty)$ // Izvestiya vuzov. Matematika, 1993, # 11(378), s. 57–61.
O skhodimosti interpolyatsionnogo protsessa Lagranzha–Ermita dlya neogranichennykh funktsii // Analysis Mathematica, 1994, # 20, p. 295–308.
Ob odnom polinomialnom neravenstve G. Froida // Matematicheskie zametki, 1996, t. 60, vyp. 5, s. 788–792.
O norme minimalnogo lineinogo proektora v $C[0,\infty)$ // Izvestiya vuzov. Matematika, 1999, # 10(449), s. 31–36.
O beskonechno-konechnykh neravenstvakh, svyazannykh s vesom Lagerra // Matematicheskie zametki, 2001, t. 70, vyp. 2, s. 260–269.
