Global Smoothness Preservation by Algebraic Interpolation Operators [PDF]
, 2000 Let {Ln(f)}n be a sequence of approximation algebraic operators, applied to a non-periodic function f ∈ C[a, b]. When {Ln(f)}n does not preserve the global smoothness of f,a natural question arises: how much of the global smoothness of f is preserved by {L n (f)} n ?
Gal Sorin G
exaly +3 more sources
Other Applications of the Global Smoothness Preservation Property [PDF]
, 2000 In this last chapter we discuss some implications of the global smoothness preservation phenomenon in various fields of mathematics.
Gal Sorin G
exaly +3 more sources
General Theory of Global Smoothness Preservation by Univariate Singular Operators [PDF]
, 2000 In this chapter we show that the well-known singular integrals of Picard, Poisson-Cauchy, Gauss-Weierstrass and their Jackson type generalizations satisfy the “global smoothness preservation” property. I.e., they “ripple” less than the function they are applied on, that is producing a nice and fit approximation to the unit.
Gal Sorin G
exaly +5 more sources
Miscellaneous Progress in Global Smoothness Preservation [PDF]
, 2000 Gal Sorin G
exaly +3 more sources
Global Smoothness Preservation and Simultaneous Approximation by Multivariate Generalized Discrete Singular Operators [PDF]
Series on Concrete and Applicable Mathematics, 2016 In this chapter we study the multivariate generalized discrete singular operators defined on ℝN, N ≥ 1, regarding their simultaneous global smoothness preservation property with respect to Lp-norm for 1 ≤ p ≤ ∞, by using higher order moduli of smoothness.
Kester, Merve, Anastassiou, George A.
exaly +3 more sources
Stochastic Global Smoothness Preservation [PDF]
, 2000 Let (Ω, A,P) be a probability space and let CΩ[a, b]denote the space of stochastically continuous stochastic processes with index set [a,b]. When C [a,b] ⊂ V ⊂ CΩ[a,b] and \( \tilde L:V \to C_\Omega \left[ {a,b} \right] \) is an E(expectation)-commutative linear operator on V, sufficient conditions are given here for E-preservation of global smoothness
George A. Anastassiou, Sorin G. Gal
openaire +2 more sources
General Theory of Global Smoothness Preservation by Singular Integrals, Univariate Case [PDF]
Journal of Computational Analysis and Applications, 1999 The authors consider the well-known singular integral of Picard in spaces \(L^p({\mathbb R})\), \(1 \leq p \leq \infty\), the well-known singular integrals of Poisson-Cauchy and Gauss-Weierstrass in spaces \(L^p_{2\pi}\), \(1 \leq p \leq \infty\), \(C_{2\pi}\), their Jackson-type generalizations, and the singular integral \[ (L_{\xi}f)(x) = \frac{1 ...
Anastassiou, George A., Gal, Sorin G.
openaire +2 more sources
Gonska Progress in Global Smoothness Preservation [PDF]
, 2000 Here global smoothness is mainly expressed by the Peetre K-functional of order s ≥1, defined by $$ \begin{gathered} K_S \left( {f,\delta } \right): = K\left( {f;\delta ;C\left( {\left[ {0,1} \right]} \right),C^s \left( {\left[ {0,1} \right]} \right)} \right) \hfill \\ : = \inf \left\{ {\parallel f - g\parallel _\infty :g \in C^s \left( {\left[ {0,1}
George A. Anastassiou, Sorin G. Gal
openaire +2 more sources
Global Smoothness Preservation by Trigonometric Operators [PDF]
, 2000 Let {Tn(f)}n be a sequence of trigonometric approximation operators applied to a continuous periodic function f ∈ C2π.
George A. Anastassiou, Sorin G. Gal
openaire +2 more sources
Global Smoothness Preservation by Blossoms of Bernstein Polynomials [PDF]
, 1995 exaly +3 more sources