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Journal articles on the topic 'Sampling Kantorovich'

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Published: 10 March 2023

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1

Tabatabaie, Seyyed Mohammad, A. Sathish Kumar, and Mahmood Pourgholamhossein. "Generalized Kantorovich sampling type series on hypergroups." Novi Sad Journal of Mathematics 48, no. 1 (January 9, 2018): 117–27. http://dx.doi.org/10.30755/nsjom.07047.

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2

Bajpeyi, Shivam, and A. Sathish Kumar. "On Approximation by Kantorovich Exponential Sampling Operators." Numerical Functional Analysis and Optimization 42, no. 9 (June 21, 2021): 1096–113. http://dx.doi.org/10.1080/01630563.2021.1940200.

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3

Costarelli, Danilo, and Gianluca Vinti. "Order of approximation for sampling Kantorovich operators." Journal of Integral Equations and Applications 26, no. 3 (September 2014): 345–67. http://dx.doi.org/10.1216/jie-2014-26-3-345.

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4

Costarelli, Danilo, and Gianluca Vinti. "An Inverse Result of Approximation by Sampling Kantorovich Series." Proceedings of the Edinburgh Mathematical Society 62, no. 1 (October 16, 2018): 265–80. http://dx.doi.org/10.1017/s0013091518000342.

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AbstractIn the present paper, an inverse result of approximation, i.e. a saturation theorem for the sampling Kantorovich operators, is derived in the case of uniform approximation for uniformly continuous and bounded functions on the whole real line. In particular, we prove that the best possible order of approximation that can be achieved by the above sampling series is the order one, otherwise the function being approximated turns out to be a constant. The above result is proved by exploiting a suitable representation formula which relates the sampling Kantorovich series with the well-known generalized sampling operators introduced by Butzer. At the end, some other applications of such representation formulas are presented, together with a discussion concerning the kernels of the above operators for which such an inverse result occurs.

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5

Costarelli, Danilo, Anna Maria Minotti, and Gianluca Vinti. "Approximation of discontinuous signals by sampling Kantorovich series." Journal of Mathematical Analysis and Applications 450, no. 2 (June 2017): 1083–103. http://dx.doi.org/10.1016/j.jmaa.2017.01.066.

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6

Angamuthu, Sathish Kumar, and Devaraj Ponnaian. "Approximation by generalized bivariate Kantorovich sampling type series." Journal of Analysis 27, no. 2 (May 24, 2018): 429–49. http://dx.doi.org/10.1007/s41478-018-0085-6.

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7

Angeloni, Laura, Danilo Costarelli, Marco Seracini, Gianluca Vinti, and Luca Zampogni. "Variation diminishing-type properties for multivariate sampling Kantorovich operators." Bollettino dell'Unione Matematica Italiana 13, no. 4 (August 27, 2020): 595–605. http://dx.doi.org/10.1007/s40574-020-00256-3.

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Abstract In this paper we establish a variation-diminishing type estimate for the multivariate Kantorovich sampling operators with respect to the concept of multidimensional variation introduced by Tonelli. A sharper estimate can be achieved when step functions with compact support (digital images) are considered. Several examples of kernels have been presented.

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8

Orlova, Olga, and Gert Tamberg. "On approximation properties of generalized Kantorovich-type sampling operators." Journal of Approximation Theory 201 (January 2016): 73–86. http://dx.doi.org/10.1016/j.jat.2015.10.001.

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9

Bartoccini, Benedetta, Danilo Costarelli, and Gianluca Vinti. "Extension of Saturation Theorems for the Sampling Kantorovich Operators." Complex Analysis and Operator Theory 13, no. 3 (October 9, 2018): 1161–75. http://dx.doi.org/10.1007/s11785-018-0852-z.

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10

Bardaro, Carlo, and Ilaria Mantellini. "Asymptotic formulae for multivariate Kantorovich type generalized sampling series." Acta Mathematica Sinica, English Series 27, no. 7 (June 15, 2011): 1247–58. http://dx.doi.org/10.1007/s10114-011-0227-0.

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11

ACAR, TUNCER, OSMAN ALAGÖZ, ALİ ARAL, DANİLO COSTARELLİ, METİN TURGAY, and GIANLUCA VINTI. "Approximation by sampling Kantorovich series in weighted spaces of functions." Turkish Journal of Mathematics 46, no. 7 (January 1, 2022): 2663–76. http://dx.doi.org/10.55730/1300-0098.3293.

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12

Costarelli, Danilo, Pietro Pozzilli, Marco Seracini, and Gianluca Vinti. "Enhancement of Cone-Beam Computed Tomography Dental-Maxillofacial Images by Sampling Kantorovich Algorithm." Symmetry 13, no. 8 (August 9, 2021): 1450. http://dx.doi.org/10.3390/sym13081450.

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In this paper, we establish a procedure for the enhancement of cone-beam computed tomography (CBCT) dental-maxillofacial images; this can be useful in order to face the problem of rapid prototyping, i.e., to generate a 3D printable file of a dental prosthesis. In the proposed procedure, a crucial role is played by the so-called sampling Kantorovich (SK) algorithm for the reconstruction and image noise reduction. For the latter algorithm, it has already been shown to be effective in the reconstruction and enhancement of real-world images affected by noise in connection to engineering and biomedical problems. The SK algorithm is given by an optimized implementation of the well-known sampling Kantorovich operators and their approximation properties. A comparison between CBTC images processed by the SK algorithm and other well-known methods of digital image processing known in the literature is also given. We finally remark that the above-treated topic has a strong multidisciplinary nature and involves concrete biomedical applications of mathematics. In this type of research, theoretical and experimental disciplines merge in order to find solutions to real-world problems.

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13

Bardaro, C., G. Vinti, P. L. Butzer, and R. L. Stens. "Kantorovich-Type Generalized Sampling Series in the Setting of Orlicz Spaces." Sampling Theory in Signal and Image Processing 6, no. 1 (January 2007): 29–52. http://dx.doi.org/10.1007/bf03549462.

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14

Costarelli, Danilo, and Gianluca Vinti. "Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces." Journal of Integral Equations and Applications 26, no. 4 (December 2014): 455–81. http://dx.doi.org/10.1216/jie-2014-26-4-455.

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15

Vinti, Gianluca, and Luca Zampogni. "Approximation by means of nonlinear Kantorovich sampling type operators in Orlicz spaces." Journal of Approximation Theory 161, no. 2 (December 2009): 511–28. http://dx.doi.org/10.1016/j.jat.2008.11.011.

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16

Costarelli, Danilo, and Gianluca Vinti. "Approximation by Nonlinear Multivariate Sampling Kantorovich Type Operators and Applications to Image Processing." Numerical Functional Analysis and Optimization 34, no. 8 (August 3, 2013): 819–44. http://dx.doi.org/10.1080/01630563.2013.767833.

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17

Costarelli, Danilo, and Gianluca Vinti. "Degree of Approximation for Nonlinear Multivariate Sampling Kantorovich Operators on Some Functions Spaces." Numerical Functional Analysis and Optimization 36, no. 8 (May 21, 2015): 964–90. http://dx.doi.org/10.1080/01630563.2015.1040888.

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18

Costarelli, Danilo, and Gianluca Vinti. "Inverse results of approximation and the saturation order for the sampling Kantorovich series." Journal of Approximation Theory 242 (June 2019): 64–82. http://dx.doi.org/10.1016/j.jat.2019.03.001.

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19

Acar, Tuncer, Danilo Costarelli, and Gianluca Vinti. "Linear prediction and simultaneous approximation by m-th order Kantorovich type sampling series." Banach Journal of Mathematical Analysis 14, no. 4 (May 28, 2020): 1481–508. http://dx.doi.org/10.1007/s43037-020-00071-0.

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20

Costarelli, Danilo, and Gianluca Vinti. "Multivariate sampling Kantorovich operators: from the theory to the Digital Image Processing algorithm." PAMM 15, no. 1 (October 2015): 655–56. http://dx.doi.org/10.1002/pamm.201510317.

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21

Cantarini, Marco, Danilo Costarelli, and Gianluca Vinti. "Approximation of differentiable and not differentiable signals by the first derivative of sampling Kantorovich operators." Journal of Mathematical Analysis and Applications 509, no. 1 (May 2022): 125913. http://dx.doi.org/10.1016/j.jmaa.2021.125913.

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22

Costarelli, Danilo, and Gianluca Vinti. "Saturation by the Fourier transform method for the sampling Kantorovich series based on bandlimited kernels." Analysis and Mathematical Physics 9, no. 4 (July 13, 2019): 2263–80. http://dx.doi.org/10.1007/s13324-019-00334-6.

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23

Coroianu, Lucian, and Sorin G. Gal. "$L^p$-approximation by truncated max-product sampling operators of Kantorovich-type based on Fejér kernel." Journal of Integral Equations and Applications 29, no. 2 (April 2017): 349–64. http://dx.doi.org/10.1216/jie-2017-29-2-349.

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24

Cagini, C., D. Costarelli, R. Gujar, M. Lupidi, G. A. Lutty, M. Seracini, and G. Vinti. "Improvement of retinal OCT angiograms by Sampling Kantorovich algorithm in the assessment of retinal and choroidal perfusion." Applied Mathematics and Computation 427 (August 2022): 127152. http://dx.doi.org/10.1016/j.amc.2022.127152.

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25

Cagini, C., D. Costarelli, R. Gujar, M. Lupidi, G. A. Lutty, M. Seracini, and G. Vinti. "Improvement of retinal OCT angiograms by Sampling Kantorovich algorithm in the assessment of retinal and choroidal perfusion." Applied Mathematics and Computation 427 (August 2022): 127152. http://dx.doi.org/10.1016/j.amc.2022.127152.

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26

Costarelli, Danilo, Marco Seracini, and Gianluca Vinti. "A comparison between the sampling Kantorovich algorithm for digital image processing with some interpolation and quasi-interpolation methods." Applied Mathematics and Computation 374 (June 2020): 125046. http://dx.doi.org/10.1016/j.amc.2020.125046.

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27

Magini, Roberto, Maria Boniforti, and Roberto Guercio. "Generating Scenarios of Cross-Correlated Demands for Modelling Water Distribution Networks." Water 11, no. 3 (March 8, 2019): 493. http://dx.doi.org/10.3390/w11030493.

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A numerical approach for generating a limited number of water demand scenarios and estimating their occurrence probabilities in a water distribution network (WDN) is proposed. This approach makes use of the demand scaling laws in order to consider the natural variability and spatial correlation of nodal consumption. The scaling laws are employed to determine the statistics of nodal consumption as a function of the number of users and the main statistical features of the unitary user’s demand. Besides, consumption at each node is considered to follow a Gamma probability distribution. A high number of groups of cross-correlated demands, i.e., scenarios, for the entire network were generated using Latin hypercube sampling (LHS) and the numerical procedure proposed by Iman and Conover. The Kantorovich distance is used to reduce the number of scenarios and estimate their corresponding probabilities, while keeping the statistical information on nodal consumptions. By hydraulic simulation, the whole number of generated demand scenarios was used to obtain a corresponding number of pressure scenarios on which the same reduction procedure was applied. The probabilities of the reduced scenarios of pressure were compared with the corresponding probabilities of demand.

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28

Çetin, Nursel, Danilo Costarelli, and Gianluca Vinti. "Quantitative Estimates for Nonlinear Sampling Kantorovich Operators." Results in Mathematics 76, no. 2 (April 2, 2021). http://dx.doi.org/10.1007/s00025-021-01383-9.

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AbstractIn this paper, we establish quantitative estimates for nonlinear sampling Kantorovich operators in terms of the modulus of smoothness in the setting of Orlicz spaces. This general frame allows us to directly deduce some quantitative estimates of approximation in $$L^{p}$$ L p -spaces, $$1\le p<\infty $$ 1 ≤ p < ∞ , and in other well-known instances of Orlicz spaces, such as the Zygmung and the exponential spaces. Further, the qualitative order of approximation has been obtained assuming f in suitable Lipschitz classes. The above estimates achieved in the general setting of Orlicz spaces, have been also improved in the $$L^p$$ L p -case, using a direct approach suitable to this context. At the end, we consider the particular cases of the nonlinear sampling Kantorovich operators constructed by using some special kernels.

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29

Angeloni, Laura, Danilo Costarelli, and Gianluca Vinti. "Approximation properties of mixed sampling-Kantorovich operators." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 115, no. 1 (October 11, 2020). http://dx.doi.org/10.1007/s13398-020-00936-x.

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Abstract In the present paper we study the pointwise and uniform convergence properties of a family of multidimensional sampling Kantorovich type operators. Moreover, besides convergence, quantitative estimates and a Voronovskaja type theorem have been established.

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30

Acar, Tuncer, Sadettin Kursun, and Metin Turgay. "Multidimensional Kantorovich modifications of exponential sampling series." Quaestiones Mathematicae, January 14, 2022, 1–16. http://dx.doi.org/10.2989/16073606.2021.1992033.

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31

Aral, Ali, Tuncer Acar, and Sadettin Kursun. "Generalized Kantorovich forms of exponential sampling series." Analysis and Mathematical Physics 12, no. 2 (March 12, 2022). http://dx.doi.org/10.1007/s13324-022-00667-9.

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32

Costarelli, Danilo, and Gianluca Vinti. "Approximation Properties of the Sampling Kantorovich Operators: Regularization, Saturation, Inverse Results and Favard Classes in $$L^p$$-Spaces." Journal of Fourier Analysis and Applications 28, no. 3 (May 17, 2022). http://dx.doi.org/10.1007/s00041-022-09943-5.

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AbstractIn the present paper, a characterization of the Favard classes for the sampling Kantorovich operators based upon bandlimited kernels has been established. In order to achieve the above result, a wide preliminary study has been necessary. First, suitable high order asymptotic type theorems in $$L^p$$ L p -setting, $$1 \le p \le +\infty $$ 1 ≤ p ≤ + ∞ , have been proved. Then, the regularization properties of the sampling Kantorovich operators have been investigated. Here, we show how the regularity of the kernel influences the operator itself; this has been shown for bandlimited kernels, or more in general for kernels in Sobolev spaces, satisfying a Strang-Fix type condition of order $$r \in \mathbb {N}^+$$ r ∈ N + . Further, for the order of approximation of the sampling Kantorovich operators, quantitative estimates based on the $$L^p$$ L p modulus of smoothness of order r have been established. As a consequence, the qualitative order of approximation is also derived assuming f in suitable Lipschitz and generalized Lipschitz classes. Moreover, an inverse theorem of approximation has been stated, allowing to obtain a full characterization of the Lipschitz and of the generalized Lipschitz classes in terms of convergence of the above sampling type series. These approximation results have been proved for not necessarily bandlimited kernels. From the above mentioned characterization, it remains uncovered the saturation case that, however, can be treated by a totally different approach assuming that the kernel is bandlimited. Indeed, since sampling Kantorovich (discrete) operators based upon bandlimited kernels can be viewed as double-singular integrals, exploiting the properties of the convolution in Fourier Analysis, we become able to get the desired result obtaining a complete overview of the approximation properties in $$L^p(\mathbb {R})$$ L p ( R ) , $$1 \le p \le +\infty $$ 1 ≤ p ≤ + ∞ , for the sampling Kantorovich operators.

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33

ANGELONİ, Laura, Nursel ÇETİN, Danilo COSTARELLI, Anna Rita SAMBUCİNİ, and Gianluca VINTI. "Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces." Constructive Mathematical Analysis, February 16, 2021. http://dx.doi.org/10.33205/cma.876890.

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34

Kumar, A. Sathish, Prashant Kumar, and P. Devaraj. "Approximation of discontinuous functions by Kantorovich exponential sampling series." Analysis and Mathematical Physics 12, no. 3 (April 12, 2022). http://dx.doi.org/10.1007/s13324-022-00680-y.

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35

Angamuthu, Sathish Kumar, and Shivam Bajpeyi. "Direct and Inverse Results for Kantorovich Type Exponential Sampling Series." Results in Mathematics 75, no. 3 (July 9, 2020). http://dx.doi.org/10.1007/s00025-020-01241-0.

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36

Coroianu, Lucian, Danilo Costarelli, Sorin G. Gal, and Gianluca Vinti. "Approximation by max-product sampling Kantorovich operators with generalized kernels." Analysis and Applications, August 18, 2019, 1–26. http://dx.doi.org/10.1142/s0219530519500155.

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In a recent paper, for max-product sampling operators based on general kernels with bounded generalized absolute moments, we have obtained several pointwise and uniform convergence properties on bounded intervals or on the whole real axis, including a Jackson-type estimate in terms of the first uniform modulus of continuity. In this paper, first, we prove that for the Kantorovich variants of these max-product sampling operators, under the same assumptions on the kernels, these convergence properties remain valid. Here, we also establish the [Formula: see text] convergence, and quantitative estimates with respect to the [Formula: see text] norm, [Formula: see text]-functionals and [Formula: see text]-modulus of continuity as well. The results are tested on several examples of kernels and possible extensions to higher dimensions are suggested.

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37

Costarelli, Danilo, and Gianluca Vinti. "Convergence of sampling Kantorovich operators in modular spaces with applications." Rendiconti del Circolo Matematico di Palermo Series 2, August 9, 2020. http://dx.doi.org/10.1007/s12215-020-00544-z.

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Abstract In the present paper we study the so-called sampling Kantorovich operators in the very general setting of modular spaces. Here, modular convergence theorems are proved under suitable assumptions, together with a modular inequality for the above operators. Further, we study applications of such approximation results in several concrete cases, such as Musielak–Orlicz and Orlicz spaces. As a consequence of these results we obtain convergence theorems in the classical and weighted versions of the $$L^p$$ L p and Zygmund (or interpolation) spaces. At the end of the paper examples of kernels for the above operators are presented.

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38

Kumar, A. Sathish, and Bajpeyi Shivam. "Inverse approximation and GBS of bivariate Kantorovich type sampling series." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 114, no. 2 (January 27, 2020). http://dx.doi.org/10.1007/s13398-020-00805-7.

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39

Vinti, Gianluca, and Luca Zampogni. "Approximation Results for a General Class of Kantorovich Type Operators." Advanced Nonlinear Studies 14, no. 4 (January 1, 2014). http://dx.doi.org/10.1515/ans-2014-0410.

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AbstractWe introduce and study a family of integral operators in the Kantorovich sense acting on functions defined on locally compact topological groups. We obtain convergence results for the above operators with respect to the pointwise and uniform convergence and in the setting of Orlicz spaces with respect to the modular convergence. Moreover, we show how our theory applies to several classes of integral and discrete operators, as sampling, convolution and Mellin type operators in the Kantorovich sense, thus obtaining a simultaneous approach for discrete and integral operators. Further, we obtain general convergence results in particular cases of Orlicz spaces, as L

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40

Costarelli, Danilo, and Gianluca Vinti. "Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces." Commentationes Mathematicae 53, no. 2 (December 15, 2013). http://dx.doi.org/10.14708/cm.v53i2.792.

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41

Kolomoitsev, Yurii, Tetiana Lomako, and Sergey Tikhonov. "Sparse Grid Approximation in Weighted Wiener Spaces." Journal of Fourier Analysis and Applications 29, no. 2 (February 24, 2023). http://dx.doi.org/10.1007/s00041-023-09994-2.

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AbstractWe study approximation properties of multivariate periodic functions from weighted Wiener spaces by sparse grid methods constructed with the help of quasi-interpolation operators. The class of such operators includes classical interpolation and sampling operators, Kantorovich-type operators, scaling expansions associated with wavelet constructions, and others. We obtain the rate of convergence of the corresponding sparse grid methods in weighted Wiener norms as well as analogues of the Littlewood–Paley-type characterizations in terms of families of quasi-interpolation operators.

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42

Angeloni, Laura, Danilo Costarelli, and Gianluca Vinti. "A Characterization of the Absolute Continuity in Terms of Convergence in Variation for the Sampling Kantorovich Operators." Mediterranean Journal of Mathematics 16, no. 2 (March 1, 2019). http://dx.doi.org/10.1007/s00009-019-1315-0.

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43

Ayan, Serkan, and Nurhayat İspir. "Convergence theorems in Orlicz and Bögel continuous functions spaces by means of Kantorovich discrete type sampling operators." Mathematical Foundations of Computing, 2022, 0. http://dx.doi.org/10.3934/mfc.2022056.

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44

Costarelli, Danilo, and Gianluca Vinti. "A Quantitative Estimate for the Sampling Kantorovich Series in Terms of the Modulus of Continuity in Orlicz Spaces." Constructive Mathematical Analysis, March 1, 2019, 8–14. http://dx.doi.org/10.33205/cma.484500.

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