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Quasi Extended Chebyshev spaces and weight functions
Numerische Mathematik, 2010The main result shows that the converse for any quasi extended Chebysev space on the closed bounded interval \([a,b]\) is a quasi complete W-space on \([a,b]\). In the third section the author gives a proof of the result and some implications, such as the existence of Bernstein-type operators and integral recurrence relations for Bernstein-type bases.
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INTERPOLATION OF CHEBYSHEV POLYNOMIALS AND INTERACTING FOCK SPACES
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2006We discover a family of probability measures μa, 0 < a ≤ 1, [Formula: see text] which contains the arcsine distribution (a = 1) and semi-circle distribution (a = 1/2). We show that the multiplicative renormalization method can be used to produce orthogonal polynomials, called Chebyshev polynomials with one parameter a, which reduce to Chebyshev ...
Kubo, Izumi +2 more
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Bernstein-type operators in Chebyshev spaces
Numerical Algorithms, 2009Let \(I\) denote a real interval with a non-empty interior. An \((n+1)\)-dimensional space \(E_n\subset C^n(I)\) is said to be an extended Chebyshev space on \(I\) if any non-zero element of \(E_n\) vanishes at most \(n\) times in \(I\), counting multiplicities as far as possible for \(C^n\) functions, that is, up to \((n+1)\).
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Bounded Chebyshev sets in finite-dimensional Banach spaces
Mathematical Notes of the Academy of Sciences of the USSR, 1984Several necessary and sufficient conditions for all bounded Chebyshev sets in a finite dimensional Banach space to be convex are given. For instance, one such condition is that in the dual sphere the extremal points should form a dense subset. This answers a question raised by Stechkin.
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On dimension elevation in Quasi Extended Chebyshev spaces
Numerische Mathematik, 2008The present paper is motivated by one of the results on a dimension elevation process involving numbers \(p, q\) and a chosen integer \(n\) with \(p=q \geq 3\) and \(2 \leq n \leq p-1 \), proved by \textit{P. Costantini, T. Lyche} and \textit{C. Manni} [Numer. Math. 101, No. 2, 333--354 (2005; Zbl 1085.41002)].
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Chebyshev’s inequality for Hilbert-space-valued random elements
Statistics & Probability Letters, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Chebyshev centers and ?-normal spaces
Mathematical Notes of the Academy of Sciences of the USSR, 1981V. N. Zamyatin, A. B. Shishkin
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