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].