Chebyshev series expansions of the functions and
Z. Cylkowski (1966)
Applicationes Mathematicae
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Z. Cylkowski (1966)
Applicationes Mathematicae
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Hacène Belbachir, Farid Bencherif (2008)
Discussiones Mathematicae - General Algebra and Applications
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Letting (resp. ) be the n-th Chebyshev polynomials of the first (resp. second) kind, we prove that the sequences and for n - 2⎣n/2⎦ ≤ k ≤ n - ⎣n/2⎦ are two basis of the ℚ-vectorial space formed by the polynomials of ℚ[X] having the same parity as n and of degree ≤ n. Also and admit remarkableness integer coordinates on each of the two basis.
T. Alden Gassert (2014)
Journal de Théorie des Nombres de Bordeaux
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Let be any integer and fix an odd prime . Let denote the -fold composition of the Chebyshev polynomial of degree shifted by . If this polynomial is irreducible, let , where is a root of . We use a theorem of Dedekind in conjunction with previous results of the author to give conditions on that ensure is monogenic. For other values of , we apply a result of Guàrdia, Montes, and Nart to obtain a formula for the discriminant of and compute an integral basis for the ring...
Łukasz Piasecki (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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The aim of this paper is to show that for every Banach space containing asymptotically isometric copy of the space there is a bounded, closed and convex set with the Chebyshev radius such that for every there exists a -contractive mapping with for any .
Jon Eivind Vatne (2017)
Applications of Mathematics
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Acute triangles are defined by having all angles less than , and are characterized as the triangles containing their circumcenter in the interior. For simplices of dimension , acuteness is defined by demanding that all dihedral angles between -dimensional faces are smaller than . However, there are, in a practical sense, too few acute simplices in general. This is unfortunate, since the acuteness property provides good qualitative features for finite element methods. The property...
Jiří Matoušek, Martin Tancer, Uli Wagner (2011)
Journal of the European Mathematical Society
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Let be the following algorithmic problem: Given a finite simplicial complex of dimension at most , does there exist a (piecewise linear) embedding of into ? Known results easily imply polynomiality of (; the case is graph planarity) and of for all . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that and are undecidable for each . Our main result is NP-hardness of and, more generally, of for all...
Jean Schmets, Manuel Valdivia (2005)
Annales Polonici Mathematici
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We deal with projective limits of classes of functions and prove that: (a) the Chebyshev polynomials constitute an absolute Schauder basis of the nuclear Fréchet spaces ; (b) there is no continuous linear extension map from into ; (c) under some additional assumption on , there is an explicit extension map from into by use of a modification of the Chebyshev polynomials. These results extend the corresponding ones obtained by Beaugendre in [1] and [2].
Dušan Pokorný, Luděk Zajíček (2022)
Czechoslovak Mathematical Journal
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We give a complete characterization of closed sets whose distance function is DC (i.e., is the difference of two convex functions on ). Using this characterization, a number of properties of such sets is proved.
Jan Brandts, Abdullah Cihangir (2019)
Applications of Mathematics
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A -simplex is the convex hull of affinely independent vertices of the unit -cube . It is nonobtuse if none of its dihedral angles is obtuse, and acute if additionally none of them is right. Acute -simplices in can be represented by -matrices of size whose Gramians have an inverse that is strictly diagonally dominant, with negative off-diagonal entries. In this paper, we will prove that the positive part of the transposed inverse of is doubly stochastic and has the...
Brandts, Jan, Cihangir, Apo
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This paper is about -triangles, which are the simplest nontrivial examples of -polytopes: convex hulls of a subset of vertices of the unit -cube . We consider the subclasses of right -triangles, and acute -triangles, which only have acute angles. They can be explicitly counted and enumerated, also modulo the symmetries of .
Th. Friedrich (1974)
Colloquium Mathematicae
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Dalík, Josef
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The general method of averaging for the superapproximation of an arbitrary partial derivative of a smooth function in a vertex of a simplicial triangulation of a bounded polytopic domain in for any is described and its complexity is analysed.
Tamás Erdélyi (2001)
Colloquium Mathematicae
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Let D and ∂D denote the open unit disk and the unit circle of the complex plane, respectively. We denote by ₙ (resp. ) the set of all polynomials of degree at most n with real (resp. complex) coefficients. We define the truncation operators Sₙ for polynomials of the form , , by , (here 0/0 is interpreted as 1). We define the norms of the truncation operators by , . Our main theorem establishes the right order of magnitude of the above norms: there is an absolute constant c₁...
Tord Sjödin (2018)
Czechoslovak Mathematical Journal
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Let be a closed subset of and let denote the metric projection (closest point mapping) of onto in -norm. A classical result of Asplund states that is (Fréchet) differentiable almost everywhere (a.e.) in in the Euclidean case . We consider the case and prove that the th component of is differentiable a.e. if and satisfies Hölder condition of order if .
Małgorzata Michalska, Maria Nowak, Paweł Sobolewski (2011)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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We give new characterizations of the analytic Besov spaces on the unit ball of in terms of oscillations and integral means over some Euclidian balls contained in .
Christian Samuel (2010)
Colloquium Mathematicae
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We show that every operator from to is compact when 1 ≤ p,q < s and that every operator from to is compact when 1/p + 1/q > 1 + 1/s.
Albert Baernstein II, Robert C. Culverhouse (2002)
Studia Mathematica
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Let , , where the are independent random vectors, each uniformly distributed on the unit sphere in ℝⁿ, and are real constants. We prove that if is majorized by in the sense of Hardy-Littlewood-Pólya, and if Φ: ℝⁿ → ℝ is continuous and bisubharmonic, then EΦ(X) ≤ EΦ(Y). Consequences include most of the known sharp Khinchin inequalities for sums of the form X. For radial Φ, bisubharmonicity is necessary as well as sufficient for the majorization inequality to always hold. Counterparts...
Krzysztof Kołodziejczyk (1987)
Colloquium Mathematicae
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Rajendra K. Sharma, Gaurav Mittal (2022)
Mathematica Bohemica
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We give the characterization of the unit group of , where is a finite field with elements for prime and denotes the special linear group of matrices having determinant over the cyclic group .