Displaying similar documents to “Weighted polynomial approximation in the complex plane.”

Weighted θ-incomplete pluripotential theory

Muhammed Ali Alan (2010)

Annales Polonici Mathematici


Weighted pluripotential theory is a rapidly developing area; and Callaghan [Ann. Polon. Math. 90 (2007)] recently introduced θ-incomplete polynomials in ℂ for n>1. In this paper we combine these two theories by defining weighted θ-incomplete pluripotential theory. We define weighted θ-incomplete extremal functions and obtain a Siciak-Zahariuta type equality in terms of θ-incomplete polynomials. Finally we prove that the extremal functions can be recovered using orthonormal polynomials...

Approximation in weighted generalized grand Lebesgue spaces

Daniyal M. Israfilov, Ahmet Testici (2016)

Colloquium Mathematicae


The direct and inverse problems of approximation theory in the subspace of weighted generalized grand Lebesgue spaces of 2π-periodic functions with the weights satisfying Muckenhoupt's condition are investigated. Appropriate direct and inverse theorems are proved. As a corollary some results on constructive characterization problems in generalized Lipschitz classes are presented.

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.

General Gagliardo Inequality and Applications to Weighted Sobolev Spaces

Antonio Avantaggiati, Paola Loreti (2009)

Bollettino dell'Unione Matematica Italiana


In this paper we obtain a more general inequality with respect to a well known inequality due to Gagliardo (see [4], [5]). The inequality contained in [4], [5] has been extended to weighted spaces, obtained as cartesian product of measurable spaces. As application, we obtain a first order weighted Sobolev inequality. This generalize a previous result obtained in [2].