Approximations by Max-Product Sampling Operators

Barnabás Bede, Lucian Coroianu and Sorin G. Gal
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Barnabás Bede: DigiPen Institute of Technology, Department of Mathematics
Lucian Coroianu: University of Oradea, Department of Mathematics and Computer Science
Sorin G. Gal: University of Oradea, Department of Mathematics and Computer Science

Chapter Chapter 8 in Approximation by Max-Product Type Operators, 2016, pp 327-392 from Springer

Abstract: Abstract In this chapter we introduce and study the max-product sampling operators, which have applications to signal theory. Due to the fact that for bounded functions with positive values, the max-product sampling operators attached to them have nice properties, all the approximation results in this chapter are stated and proved under this restriction. But as it was already mentioned in Subsection 1.1.3 , Property C, this restriction can easily be dropped by considering the construction used for the max-product Bernstein operator in Theorem 2.9.1 . More precisely, if 𝒮 W , φ ( M ) $$\mathcal{S}_{W,\varphi }^{(M)}$$ is any max-product sampling operator defined in this chapter and f : ℝ → ℝ $$f: \mathbb{R} \rightarrow \mathbb{R}$$ is bounded and of variable sign, then it is easy to see that the new operators P W , φ ( M ) ( f ) ( x ) = 𝒮 W , φ ( M ) ( f − a ) ( x ) + a $$P_{W,\varphi }^{(M)}(f)(x) = \mathcal{S}_{W,\varphi }^{(M)}(f - a)(x) + a$$ , where a

Keywords: Jackson Order; Local Inverse; Interpolation Property; Saturation Order; Obtain Approximation Results (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-34189-7_8

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