Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
16.05.1940
Keywords: polynomials orthogonal on a segment; polynomials orthogonal on a circle; trigonometric polynomials orthogonal with respect to a weight; weights with non-classical singularities; asymptotic and approximation properties of orthogonal polynomials; the best approximations of the Szeg\ddot{o} function; weight analogs of Markov, Bernstein and Jackson–Nikol'skii inequalities.
Subject:
Uniform asymptotic representations on all range of orthogonality for generalized Jacobi polynomials orthogonal on a circle or a segment and also for trigonometric are obtained. Some questions on (uniform, mean and almost everywhere) convergence of Fourier series with respect to the mentioned polynomials are investigated. Two-sided point-wise estimations (sometimes uniform asymptotic representations) in terms of the Szego function for polynomials orthonormal on a circle (and their derivatives) with respect to a weight (introduced by the author), which orders of singularities are defined by finite products of real powers of concave moduli of continuity. In some cases orders of the best approximations (by algebraic polynomials) of the corresponding Szego function are found.
Main publications:
Badkov V. M. Approksimativnye svoistva ryadov Fure po ortogonalnym polinomam // UMN, 1978, 33 (4), 51–106.
Badkov V. M. Priblizhenie funktsii v ravnomernoi metrike summami Fure po ortogonalnym polinomam // Trudy MIAN, 1980, 145, 20–62.
Badkov V. M. Ravnomernye asimptoticheskie predstavleniya ortogonalnykh polinomov // Trudy MIAN, 1983, 164, 3–36.
Badkov V. M. Asimptoticheskie i ekstremalnye svoistva ortogonalnykh polinomov // Trudy MIRAN, 1992, 198, 41–88.
Badkov V. M. Potochechnye otsenki snizu modulei proizvodnykh mnogochlena, ortogonalnogo na okruzhnosti s vesom, imeyuschim osobennosti // Matem. sbornik, 1995, 186 (6), 3–14.
