Geodesic
Best Polynomial Approximation with Linear Constraints
Canadian journal of mathematics, Tome 44 (1992) no. 6, pp. 1289-1302

Voir la notice de l'article provenant de la source Cambridge University Press

Let A be a (k + 1) × (k + 1) nonzero matrix. For polynomials p ∈ Pn, set and . Let E ⊂ C be a compact set that does not separate the plane and f be a function continuous on E and analytic in the interior of E. Set and . Our goal is to study approximation to f on E by polynomials from Bn(A). We obtain necessary and sufficient conditions on the matrix A for the convergence En(A,f) → 0 to take place. These results depend on whether zero lies inside, on the boundary or outside E and yield generalizations of theorems of Clunie, Hasson and Saff for approximation by polynomials that omit a power of z. Let be such that . We also study the asymptotic behavior of the zeros of and the asymptotic relation between En(f) and En(A,f).
DOI : 10.4153/CJM-1992-077-5
Mots-clés : 41A29 
Pan, K.; Saff, E. B. Best Polynomial Approximation with Linear Constraints. Canadian journal of mathematics, Tome 44 (1992) no. 6, pp. 1289-1302. doi: 10.4153/CJM-1992-077-5
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[BSS] Blatt, H.-P., Saff, E.B. and Simkani, M., Jentzsch -Szego type theorems for zeros of best approximatifs, J. London Math. Soc . (2) 38(1980), 307–316. Google Scholar

[CHS] Clunie, J., Hasson, M. and Saff, E.B., Approximation by polynomials that omit a power of z, Approx. Theory & its Appl. 3(1987), 63–73. Google Scholar

[N] Nersesyan, A.A., Uniform approximation with simultaneous interpolation by analytic functions, Izv. Akad. Nauk Armyan. SSR. Mat. 15(1980), 249-257.(in Russian). See also Soviet J. Contemporary Math. Anal. (4) 15(1980), 1–9. Google Scholar

[ST] Saff, E.B. and Totik, V., Behavior of polynomials of best uniform approximation, Trans. Amer. Math. Soc. 316(1988), 567–593. Google Scholar

[T] Tsuji, M., Potential Theory in Modern Function Theory, 2nd éd., Chelsea Publishing Company, New York, NY, (1958). Google Scholar

[W] Walsh, J.L., Interpolation and Approximation by Rational Functions in the Complex Domain, 5th éd., Amer. Math. Soc. Colloquium Publ. 20(1969), Providence, Rhode Island. Google Scholar

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