Interpolating Generalized Shannon Sampling Operators, Their Norms and Approximation Properties

Kivinukk, Andi; Tamberg, Gert

doi:10.1007/bf03549509

Cited by 32 publications

(11 citation statements)

References 10 publications

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“…For the sake of completeness, we must observe that the above operators S w can be reviewed as an L 1 -version of the generalized sampling operators, introduced by P.L. Butzer and his school in 1980s, and widely studied in last thirty years, see e.g., [12,14,37,36]. The sampling Kantorovich operators, as well as the generalized sampling operators, are a kind of quasi-interpolation operators, see e.g., [17,46,45,44].…”

Section: Approximation By Sampling Kantorovich Operators and Applicat...mentioning

confidence: 99%

Detection of thermal bridges from thermographic images by means of image processing approximation algorithms

Asdrubali

Baldinelli

Bianchi

et al. 2018

Applied Mathematics and Computation

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Section: Approximation By Sampling Kantorovich Operators and Applicat...mentioning

confidence: 99%

Detection of thermal bridges from thermographic images by means of image processing approximation algorithms

Asdrubali

Baldinelli

Bianchi

et al. 2018

Applied Mathematics and Computation

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“…Other examples of bandlimited kernels are provided, e.g., by the Bochner-Riesz kernels ( [32]), defined by: By following the above procedure, several examples of kernels for which the previous theory holds can be given, see e.g., [30,22,25,5,6].…”

Section: Now Let Us Denote Bymentioning

confidence: 99%

“…Results about variation of the generalized sampling series were previously studied in some particular cases: for example, the variation detracting property was obtained for some kind of bandlimited kernel functions ( [25,23,24,29]), but the topic was never faced in a general setting.…”

Section: Introductionmentioning

confidence: 99%

A characterization of the convergence in variation for the generalized sampling series

Angeloni¹,

Costarelli²,

Vinti³

2018

Ann. Acad. Sci. Fenn. Math.

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In this paper, we study the convergence in variation for the generalized sampling operators based upon averaged-type kernels and we obtain a characterization of absolutely continuous functions. This result is proved exploiting a relation between the first derivative of the above operator acting on f and the sampling Kantorovich series of f . By such approach, also a variation detracting-type property is established. Finally, examples of averaged kernels are provided, such as the central B-splines of order n (duration limited functions) or other families of kernels generated by the Fejér and the Bochner-Riesz kernels (bandlimited functions).

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“…We first show ⊆ in (4.1.36). If ϕ ∈ L 2 (0, 1), then we may apply Shannon's sampling theorem [KT09] to…”

Section: 124)mentioning

confidence: 99%

Harmonic analysis of a class of reproducing kernel Hilbert spaces arising from groups

Jørgensen¹,

Pedersen²,

Tian³

2015

Trends in Harmonic Analysis and Its Applications

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Chapter 1. Introduction 1.1. Two Extension Problems 1.2. Stochastic Processes 1.3. Earlier Papers 1.4. Organization 1.5. Notation and Preliminaries 1.6. Overview of Applications of RKHSs Chapter 2. Extensions of Continuous Positive Definite Functions 2.1. Enlarging the Hilbert Space 2.2. Ext 1 (F ) and Ext 2 (F ) 2.3. Preliminaries 2.4. The Case of Locally Compact Abelian Groups 2.5. The Case of G = R n 2.6. Lie Groups 2.7. The Circle Group T 2.8. Example: e i2πx 2.9. Example: e −a|x| 2.10. The Example e −|x| in (−a, a) 2.11. Discussion Chapter 3. Type I v.s. Type II Extensions 3.1. Polya Extensions 3.2. The Example 3.1.5 Chapter 4. The Computation of Ext 1 (F ) 4.1. Mercer Operators, and Bessel Frames 4.2. Positive Definite Functions, Green's Functions, and Boundary 4.3. The RKHSs for the Two Examples F 2 and F 3 in Table 3.1.1 4.4. Higher Dimensions Chapter 5. Comparing Different RKHSs H F and H K 5.1. Applications 5.2. Radially Symmetric Positive Definite Functions 5.3. Connecting F and F When F is a Positive Definite Function 5.4. The Imaginary Part of a Positive Definite Function Chapter 6. Convolution Products Chapter 7. Models for Operator Extensions 7.1. Model for Restrictions of Continuous p.d. Functions on R 8.3. The Case of G = R 1 8.4. The Extreme Points of Ext (F ) and {F }

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Interpolating Generalized Shannon Sampling Operators, Their Norms and Approximation Properties

Cited by 32 publications

References 10 publications

Detection of thermal bridges from thermographic images by means of image processing approximation algorithms

Detection of thermal bridges from thermographic images by means of image processing approximation algorithms

A characterization of the convergence in variation for the generalized sampling series

Harmonic analysis of a class of reproducing kernel Hilbert spaces arising from groups

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