Uniform approximation by polynomials with integer coefficients
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| Title: | Uniform approximation by polynomials with integer coefficients |
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| Authors: | Lipnicki, A. |
| Source: | Opuscula Mathematica. |
| Subject Terms: | approximation by polynomials with integer coefficients, lattice, covering radius |
| Description: | Let r, n be positive integers with n ≥ 6r. Let P be a polynomial of degree at most n on [0,1] with real coefficients, such that [formula] are integers for k = 0,…, r — 1. It is proved that there is a polynomial Q of degree at most n with integer coefficients such that [formula] for x ∈ [0,1], where C1, C2 are some numerical constants. The result is the best possible up to the constants. |
| Document Type: | Article |
| Language: | English |
| Access URL: | http://yadda.icm.edu.pl/baztech/element/bwmeta1.element.baztech-7a30cfe2-973c-4dba-b15a-e9725b5ab7ac |
| Accession Number: | edsbzt.bwmeta1.element.baztech.7a30cfe2.973c.4dba.b15a.e9725b5ab7ac |
| Database: | BazTech |
| Abstract: | Let r, n be positive integers with n ≥ 6r. Let P be a polynomial of degree at most n on [0,1] with real coefficients, such that [formula] are integers for k = 0,…, r — 1. It is proved that there is a polynomial Q of degree at most n with integer coefficients such that [formula] for x ∈ [0,1], where C1, C2 are some numerical constants. The result is the best possible up to the constants. |
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