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On a Problem of Best Uniform Approximation and a Polynomial Inequality of Visser

M. A. Qazi (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

In this paper, a generalization of a result on the uniform best approximation of α cos nx + β sin nx by trigonometric polynomials of degree less than n is considered and its relationship with a well-known polynomial inequality of C. Visser is indicated.

On the approximation of entire functions over Carathéodory domains

Devendra Kumar, Harvir S. Kasana (1994)

Commentationes Mathematicae Universitatis Carolinae

Let D be a Carathéodory domain. For 1 p , let L p ( D ) be the class of all functions f holomorphic in D such that f D , p = [ 1 A D | f ( z ) | p d x d y ] 1 / p < , where A is the area of D . For f L p ( D ) , set E n p ( f ) = inf t π n f - t D , p ; π n consists of all polynomials of degree at most n . In this paper we study the growth of an entire function in terms of approximation...

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