Results 201 to 210 of about 97,608 (251)

Global Smoothness Preservation by Multivariate Operators

2000
In this chapter we discuss the global smoothness preservation by some multivariate approximating operators. By extending a fundamental result of Khan and Peters, we establish a general result for operators having the splitting property. Furthermore, we show more complete inequalities for Bernstein operators on the k-dimensional simplex and cube ...
George A. Anastassiou, Sorin G. Gal
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Stochastic Global Smoothness Preservation

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
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General Theory of Global Smoothness Preservation by Singular Integrals, Univariate Case

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.
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Global Smoothness Preservation by General Operators

2000
In this chapter we search the conditions under which global smoothness of a function f (as measured by its modulus of continuity) is preserved by the elements of general approximating sequences (L n f). As one consequence we obtain statements concerning the invariance of Lipschitz classes under operators of several types.
George A. Anastassiou, Sorin G. Gal
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Gonska Progress in Global Smoothness Preservation

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
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Global Smoothness Preservation by Trigonometric Operators

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
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Global Smoothness Preservation and Simultaneous Approximation by Multivariate General Singular Integrals

2011
In this chapter, we continue with the study of multivariate smooth general singular integral operators over R N , N ≥ 1, regarding their simultaneous global smoothness preservation property with respect to the L p norm, 1 ≤ p ≤ ∞, by involving multivariate higher order moduli of smoothness. Also, we present their multivariate simultaneous approximation
G. Anastassiou
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Global Smoothness Preservation by Algebraic Interpolation Operators

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 ?
George A. Anastassiou, Sorin G. Gal
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Other Applications of the Global Smoothness Preservation Property

2000
In this last chapter we discuss some implications of the global smoothness preservation phenomenon in various fields of mathematics.
George A. Anastassiou, Sorin G. Gal
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General Theory of Global Smoothness Preservation by Univariate Singular Operators

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.
George A. Anastassiou, Sorin G. Gal
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