Geodesic
Polynomials of Least Deviation from Zero
Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 308-313.

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A new family of polynomials of least deviation from zero is defined on the unit disk $B$. Lower bounds for best approximations in the space $L_p(B)$, $p\ge1$, are given. 
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V. A. Yudin. Polynomials of Least Deviation from Zero. Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 308-313. http://geodesic.mathdoc.fr/item/MZM_2005_78_2_a16/

[1] Chebyshev P. L., Poln. sobr. sochinenii, Izd-vo AN SSSR, M.–L., 1948

[2] Gearhart W. B., “Some Chebyshev approximations by polynomials in two variables”, J. Approx. Theory, 8 (1973), 195–209 | DOI | MR | Zbl

[3] Rivlin T. J., Shapiro H. S., “A unified approach to certain problems of approximation and minimization”, J. Soc. Indust. Appl. Math., 9 (1961), 670–699 | DOI | MR | Zbl

[4] Reimer M., Constructive Theory of Multivariate Functions. With an Application to Tomography, Bibliographisches Institut, Mannheim, 1990 | MR

[5] Bernshtein S. N., Poln. sobr. sochinenii, T. 1, Izd-vo AN SSSR, M., 1952

[6] Andreev N. N., Yudin V. A., “Naimenee uklonyayuschiesya ot nulya mnogochleny i kubaturnye formuly Chebyshevskogo tipa”, Tr. MIAN, 232, Nauka, M., 2001, 45–57 | MR | Zbl

[7] Reimer M., “On multivariate polynomials of least deviation from zero on the unit ball”, Math. Z., 153 (1977), 51–58 | DOI | MR | Zbl

[8] Bos L., “On Kergin interpolation in the disk”, J. Approx. Theory, 37 (1983), 251–261 | DOI | MR | Zbl

[9] Majer U., “On best approximation of the monomials on the unit ball of $\mathbb R^r$”, J. Approx. Theory, 72 (1998), 74–81

[10] Korkin A. N., Zolotarev E. I., “Sur un certain minimum”, Poln. sobr. soch. E. I. Zolotareva, T. 1, Izd-vo AN SSSR, L., 1931, 138–153