Các xấp xỉ liên quan đến khoảng cách Hausdorff

N. I. Akhiezer and M. G. Krein, “Best approximation of periodic differentiate functions by trigonometric sums,” Dokl. Akad. Nauk SSSR,15, 107–112 (1937). S. N. Bernshtein, Complete Works, Vol. 1 [in Russian] (1952), pp. 127–135. S. N. Bernshtein, Complete Works, Vol. 2 [in Russian] (1954), pp. 155–158. V. M. Veselinov, “Approximation with trigonometric polynomials with respect to Hausdorff distance,” Thesis, Sofia Univ. (1965). E. V. Voronovskaya, “Odd polynomials of least deviation,” Dokl. Akad. Nauk SSSR,159, No. 4, 715–718 (1964). J. Dieudonne, Fundamentals of Modern Analysis [Russian translation] (1964). A. N. Kolmogorov, “Asymptotic characteristics of certain completely bounded metric spaces,” Dokl. Akad. Nauk SSSR,108, No. 2, 385–389 (1956). A. N. Kolmogorov and V. M. Tikhomirov, “ε-Entropy and ε-capacity of sets in functional spaces,” Usp. Matem. Nauk,14, No. 2, 3–86 (1959). A. N. Kolmogorov, “On A. V. Skorokhod convergence,” Teoriya Veroyatn. i Ee Primen.,1, No. 2, 239–247 (1959). P. P. Korovkin, Linear Operators and Approximation Theory [in Russian] (1959). I. P. Natanson, Constructive Theory of Functions [in Russian] (1949). B. Penkov and Bl. Sendov, “Entropy of sets of continuous functions of many variables,” Dokl. BAN,17, No. 4, 335–337 (1964). V. A. Popov, “Approximations of functions of many variables in terms of algebraic polynomials relative to a Hausdorff metric,” Thesis [in Bulgarian], Sof. Univ. (1965). Yu. V. Prokhorov, “Convergence of random processes and the limit theorems of probability theory,” Teoriya Veroyatn. i Ee Primen.,1, No. 2, 177–238 (1956). E. Ya. Remez, General Computational Methods of Chebyshev Approximation [in Russian] (1957). Bl. Sendov, “Approximations of functions by algebraic polynomials relative to a metric of Hausdorff type,” God. na Sof. Univ., Fiz.-Matem. Fak.,55, 1–39 (1960, 1961). Bl. Sendov and B. Penkov, “ε-Entropy and ε-capacity in spaces of continuous functions,” Izv. na Matem. Inst. na BAN,6, 27–50 (1962). Bl. Sendov, “On best approximation by algebraic polynomials relative to Hausdorff distance,” God. na Sof. Univ., Fiz.-Matem. Fak.,56, 195–207 (1961, 1962). Bl. Sendov and B. Penkov, “ε-Entropy and ε-capacity of sets of continuous functions,” Vestn. Mosk. Un-ta (1),3, 15–19 (1962). Bl. Sendov, S. Dimiev, and B. Penkov, “ε-Entropy and ε-capacity of sets of continuous curves,” Vesta. Mosk. Un-ta (1),3, 20–23 (1962). Bl. Sendov, “Linear approximation methods for periodic functions relative to Hausdorff distance,” God. na Sof. Univ., Matem. Fak.,58, 107–140 (1963, 1964). Bl. Sendov, “Best approximation relative to Hausdorff distance,” God. na Sof. Univ., Matem. Fak.,59 (1964, 1965). Bl. Sendov, “Linear methods of approximating periodic functions relative to a metric of the Hausdorff type,” Dokl. Akad. Nauk SSSR,160, No. 5, 1023–1025 (1965). Bl. Sendov, “One estimate for the approximation of functions by S. N. Bernshtein polynomials,” Matematika (Kluzh),5 (27), 145–154 (1963). Bl. Sendov and B. Penkov, “Intersection in the space of a continuous function,” Izv. Matem. Inst. Bulg. Akad. Nauk (in press). Bl. Sendov, “On Fejer's interpolation process,” Izv. na Matem. in-t na BAN,9, 133–145 (1966). Bl. Sendov and V. A. Popov, “Some properties of Hausdorff metrics,” Matematika (Kluzh) (in press). Bl. Sendov,“Approximation of point sets with polynomial assymetry in the plane,” God. na Sof. Univ., Mat. Fak.,60 (1965/66) (in press). Bl. Sendov, “Convergence of the series of a linear positive operator,” God. na Sof. Univ., Mat. Fak. (in press). Bl. Sendov, “On P. P. Korovkin's theorems on the convergence of sequences of linear positive operators,” Dokl. Akad. Nauk SSSR (in press). Bl. Sendov, “Approximation by power functions relative to a Hausdorff distance,” Matem. Zametki,2, No. 1, 61–70 (1967). V. S. Spiridonov, “The convergence of one interpolation process,” Izv. na Matem. in-t na BAN,9, 219–227 (1966). V. M. Tikhomirov, “On n-dimensional diameters of certain functional classes,” Dokl. Akad. Nauk SSSR,130, 734–738 (1960). V. M. Tikhomirov, “Diameters of sets in functional spaces and the theory of best approximations,” Usp. Matem. Nauk,15, No. 3, 81–120 (1960). G. Froid and Bl. Sendov, “On one method of approximating periodic functions by trigonometric polynomials,” Trudy Matem. in-ta AN Vengrii, (A)9, No. 3, 491–494 (1964). F. Hausdorff, Set Theory [Russian translation] (1936). S. M. Yakov, “Certain questions in the theory of approximations by algebraic polynomials,” Thesis, Sofia Univ. (1963). G. F. Clements, “Entropies of sets of functions of bounded variation,” Canad. J. Math.,15, 422–432 (1963). J. Favard,“Sur les meilleurs procedes d'approximation de certains classes des functions par des polinomes trigonometriques,” Bull. Sci. Math., 61, 209–224 (1937). J. Favard, “Sur l'approximation des functions,” Bull. Sc. Math.,53, 338–352 (1938). W. Feller, “The general diffusion operator and positive preserving semi-groups in one dimension,” Ann. of Math.,60, 417 (1954). A. N. Kolmogoroff, “Über die beste Annäherung von Funktionen einer Funktionskasse,” Ann. of Math.,37, 107–111 (1936). B. Penkov and Bl. Sendov, “Hausdorffsche Metrik und Approximation,” Num. Math.,9, 214–226 (1966). T. Popovicin, “Sur l'approximation des functions convexes d'ordre suptrier,” Mathematica,10, 49–54 (1934). Bl. Sendov and B. Penkov, “On widths of the space of continuous functions,” Compt. Rend. Acad. Bulg. Sci.,17, No. 8, 689–691 (1964).