Results 11 to 20 of about 499 (64)
Best exponents in Markov's inequalities [PDF]
, 2014 By means of weakly equilibrium Cantor-type sets, solutions of two problems related to polynomial inequalities are presented: the problem by M. Baran et al. about a compact set K ⊂ C such that the Markov inequality is not valid on K with the best Markov’s
A. Goncharov
semanticscholar +3 more sources
An elementary approach to polynomial optimization on polynomial meshes [PDF]
, 2018 A polynomial mesh on a multivariate compact set or manifold is a sequence of finite norming sets for polynomials whose norming constant is independent of degree.
Vianello, Marco
core +3 more sources
Tight wavelet frames in Lebesgue and Sobolev spaces
Journal of Function Spaces, Volume 2, Issue 3, Page 227-252, 2004., 2004 We study tight wavelet frame systems in Lp(ℝd) and prove that such systems (under mild hypotheses) give atomic decompositions of Lp(ℝd) for 1≺p≺∞. We also characterize Lp(ℝd) and Sobolev space norms by the analysis coefficients for the frame. We consider Jackson inequalities for best m‐term approximation with the systems in Lp(ℝd) and prove that such ...
L. Borup +3 more
wiley +1 more source
Approximations by multivariate sublinear and Max-product operators under convexity
Demonstratio Mathematica, 2018 Here we search quantitatively under convexity the approximation of multivariate function by general multivariate positive sublinear operators with applications to multivariate Max-product operators.
Anastassiou George A.
doaj +1 more source
Shape‐preserving multivariate polynomial approximation in C[−1,1]m
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 7, Page 325-333, 2004., 2004 We construct multivariate polynomials attached to a function f of m variables, m ≥ 2 , which approximate f with Jackson‐type rate involving a multivariate Ditzian‐Totik ω2φ‐modulus and preserve some natural kinds of multivariate monotonicity and convexity of function.
Ciprian S. Gal, Sorin G. Gal
wiley +1 more source
Univariate right fractional polynomial high order monotone approximation
Demonstratio Mathematica, 2016 Let f ∈ Cr([−1,1]), r ≥ 0 and let L* be a linear right fractional differential operator such that L*(f) ≥ 0 throughout [−1,0]. We can find a sequence of polynomials Qn of degree ≤ n such that L*(Qn) ≥ 0 over [−1,0], furthermore f is approximated right ...
Anastassiou George A.
doaj +1 more source
Some exact inequalities of Hardy‐Littlewood‐Polya type for periodic functions
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 47, Page 2517-2523, 2004., 2004 We investigate the following problem: for a given A ≥ 0, find the infimum of the set of B ≥ 0 such that the inequality ‖x(k)‖22≤A‖x(r)‖22+B‖x‖22, for k, r ∈ ℕ ∪ {0}, 0 ≤ k < r, holds for all sufficiently smooth functions.
Laith Emil Azar
wiley +1 more source
Inequalities of Hardy-Littlewood-Polya type for functions of operators and their applications [PDF]
, 2015 In this paper, we derive a generalized multiplicative Hardy-Littlewood-Polya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces.
Babenko, Vladyslav +2 more
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Transformation of the second order modulus by positive linear operators
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2015 We obtain estimates for the transformation of the second order modulus of continuity by positive linear operators which satisfy certain conditions, which are common to a large class of approximation operators.
Pǎltǎnea Radu, Stan Gabriel
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Multivariate and abstract approximation theory for Banach space valued functions
Demonstratio Mathematica, 2017 Here we study quantitatively the high degree of approximation of sequences of linear operators acting on Banach space valued Fréchet differentiable functions to the unit operator, as well as other basic approximations including those under convexity ...
Anastassiou George A.
doaj +1 more source