×

A Markov inequality in several dimensions. (English) Zbl 0287.26016


MSC:

26C05 Real polynomials: analytic properties, etc.
52A40 Inequalities and extremum problems involving convexity in convex geometry
65D99 Numerical approximation and computational geometry (primarily algorithms)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Duffin, R. J.; Schaeffer, A. C., A refinement of an inequality of the brothers Markoff, Trans. Am. Math. Soc., 50, 517-528 (1941) · Zbl 0025.31403
[2] Goldstein, A. A., Constructive Real Analysis (1967), Harper and Row: Harper and Row New York · Zbl 0189.49703
[3] Hille, E.; Szegö, G.; Tamarkin, J. D., On some generalizations of a theorem of A. Markoff, Duke Math. J., 3, 729-739 (1937) · JFM 63.0314.03
[4] Hirsch, P. M., Evaluation of orthogonal polynomials and its relationship to evaluating multiple integrals, Math. Comp., 22, 280-285 (1968) · Zbl 0159.45001
[5] Jackson, D., Formal properties of orthogonal polynomials in two variables, Duke Math. J., 2, 423-434 (1936) · JFM 62.0302.02
[6] Kellogg, O. D., On bounded polynomials in several variables, Math. Zeit., 27, 55-64 (1927) · JFM 53.0082.03
[7] Markov, A., Sur une question posee par Mendeleieff, Bull. Acad. Sci. St. Petersburg, 62, 1-24 (1889)
[8] Markov, W., Uber polynome, die in einem gegebenen intervalle moglichst wenig von null abweichen, Mat. Ann., 77, 213-258 (1916) · JFM 46.0415.01
[9] Scheick, J. T., Inequalities for derivatives of polynomials of special type, J. Approx. Theor., 6, 354-358 (1972) · Zbl 0259.26012
[10] Stroud, A. H., Integration formulas and orthogonal polynomials for two variables, SIAM J. Numer. Anal., 6, 222-229 (1969) · Zbl 0177.20304
[11] Wilhelmsen, D. R., Non-negative approximate integration in several dimensions, (Ph.D. thesis (1972), Brown University)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.