### On Direct and Converse Theorems in the Theory of Weighted Poynomial Approximation.

Géza Freud (1972)

Mathematische Zeitschrift

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Géza Freud (1972)

Mathematische Zeitschrift

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Anders, Maz'ya, V. Carlsson (1994)

Mathematica Scandinavica

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Muhammed Ali Alan (2010)

Annales Polonici Mathematici

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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...

Daniyal M. Israfilov, Ahmet Testici (2016)

Colloquium Mathematicae

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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.

G. Greaves (1985)

Banach Center Publications

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B. E. Wynne, T. V. Narayana (1981)

Cahiers du Bureau universitaire de recherche opérationnelle Série Recherche

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M. A. Qazi (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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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.

S.G. Gal (1988)

Publications de l'Institut Mathématique

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W.H. SUMMERS (1971)

Mathematische Annalen

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Pérez, Dilcia, Quintana, Yamilet (2008)

Divulgaciones Matemáticas

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Portilla, Ana, Quintana, Yamilet, Rodriguez, Jose M., Touris, Eva (2006)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

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Bichegkuev, M.S. (1999)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

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Lubinsky, D.S. (2006)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

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A. Offord (1948)

Fundamenta Mathematicae

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James E. Brennan (1985)

Journal für die reine und angewandte Mathematik

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Walczak, Z. (2005)

Acta Mathematica Universitatis Comenianae. New Series

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Michael Leinert (2006)

Banach Center Publications

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Antonio Avantaggiati, Paola Loreti (2009)

Bollettino dell'Unione Matematica Italiana

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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].