• Previous Article
    On Rogosinski-type approximation processes in Banach space using the framework of the cosine operator function
  • MFC Home
  • This Issue
  • Next Article
    Cesàro summability and Lebesgue points of higher dimensional Fourier series
doi: 10.3934/mfc.2021031
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

Boundedness properties of semi-discrete sampling operators in Mellin–Lebesgue spaces

Department of Mathematics and Computer Sciences, University of Perugia, via Vanvitelli 1, I-06123 Perugia, Italy

* Corresponding author: Carlo Bardaro

Received  August 2021 Revised  October 2021 Early access November 2021

Fund Project: Carlo Bardaro and Ilaria Mantellini have been partially supported by the "Gruppo Nazionale per l'Analisi Matematica e Applicazioni (GNAMPA)" of the "Istituto di Alta Matematica (INDAM)" as well as by the projects "Ricerca di Base 2019 of University of Perugia (title: Misura, Integrazione, Approssimazione e loro Applicazioni)" and "Progetto Fondazione Cassa di Risparmio cod. nr. 2018.0419.021 (title: Metodi e Processi di Intelligenza artificiale per lo sviluppo di una banca di immagini mediche per fini diagnostici (B.I.M.))"

In this paper we study boundedness properties of certain semi-discrete sampling series in Mellin–Lebesgue spaces. Also we examine some examples which illustrate the theory developed. These results pave the way to the norm-convergence of these operators

Citation: Carlo Bardaro, Ilaria Mantellini. Boundedness properties of semi-discrete sampling operators in Mellin–Lebesgue spaces. Mathematical Foundations of Computing, doi: 10.3934/mfc.2021031
References:
[1]

L. AngeloniD. Costarelli and G. Vinti, A characterization of the convergence in variation for the generalized sampling series, Ann. Acad. Sci. Fenn. Math., 43 (2018), 755-767.  doi: 10.5186/aasfm.2018.4343.  Google Scholar

[2]

L. AngeloniD. Costarelli and G. Vinti, Convergence in variation for the multidimensional generalized sampling series and applications to smoothing for digital image processing, Ann. Acad. Sci. Fenn. Math., 45 (2020), 751-770.  doi: 10.5186/aasfm.2020.4532.  Google Scholar

[3]

F. AsdrubaliG. BaldinelliF. BianchiD. CostarelliA. RotiliM. Seracini and G. Vinti, Detection of thermal bridges from thermographic images by means of image processing approximation algorithms, Appl. Math. Comput., 317 (2018), 160-171.  doi: 10.1016/j.amc.2017.08.058.  Google Scholar

[4]

S. Balsamo and I. Mantellini, On linear combinations of general exponential sampling series, Results Math., 74 (2019), Paper No. 180, 19 pp. doi: 10.1007/s00025-019-1104-x.  Google Scholar

[5]

C. BardaroP. L. Butzer and I. Mantellini, The exponential sampling theorem of signal analysis and the reproduction kernel formula in the Mellin transform setting, Sampl. Theory Signal Image Process., 13 (2014), 35-66.  doi: 10.1007/BF03549572.  Google Scholar

[6]

C. BardaroP. L. Butzer and I. Mantellini, The Mellin-Parseval formula and its interconnections with the exponential sampling theorem of optical physics, Integral Transforms and Special Functions, 27 (2016), 17-29.  doi: 10.1080/10652469.2015.1087401.  Google Scholar

[7]

C. BardaroP. L. ButzerR. L. Stens and G. Vinti, Prediction by samples from the past with error estimates covering discontinuous signals, IEEE Trans. Information Theory, 56 (2010), 614-633.  doi: 10.1109/TIT.2009.2034793.  Google Scholar

[8]

C. BardaroL Faina and I. Mantellini, A generalization of the exponential sampling series and its approximation properties, Math. Slovaca., 67 (2017), 1481-1496.  doi: 10.1515/ms-2017-0064.  Google Scholar

[9]

C. BardaroL. Faina and I. Mantellini, Quantitative Voronovskaja formulae for generalized Durrmeyer sampling type series, Math. Nachr., 289 (2016), 1702-1720.  doi: 10.1002/mana.201500225.  Google Scholar

[10]

C. Bardaro and I. Mantellini, A quantitative Voronovskaja formula for generalized sampling operators, East J. Approx., 15 (2009), 459-471.   Google Scholar

[11]

C. Bardaro and I. Mantellini, Asymptotic formulae for linear combinations of generalized sampling type operators, Z. Anal. Anwend., 32 (2013), 279-298.  doi: 10.4171/ZAA/1485.  Google Scholar

[12]

C. Bardaro and I. Mantellini, Asymptotic expansion of generalized Durrmeyer sampling type series, Jaen Journal on Approximation, 6 (2014), 143-165.   Google Scholar

[13]

C. Bardaro and I. Mantellini, On a Durrmeyer type modifcation of the Exponential sampling series, Rend. Circ. Mat. Palermo (2), 70 (2021), 1289-1304.  doi: 10.1007/s12215-020-00559-6.  Google Scholar

[14]

C. Bardaro, I. Mantellini and G. Schmeisser, Exponential sampling series: Convergence in Mellin-Lebesgue spaces, Results Math., 74 (2019), Paper No. 119, 20 pp. doi: 10.1007/s00025-019-1044-5.  Google Scholar

[15]

C. BardaroG. VintiP. L. Butzer and R. L. Stens, Kantorovich-type generalized sampling series in the setting of Orlicz spaces, Sampling Theory Signal Image Processing, 6 (2007), 29-52.  doi: 10.1007/BF03549462.  Google Scholar

[16]

M. Bertero and E. R. Pike, Exponential sampling method for Laplace and other dilationally invariant transforms: I. Singular-system analysis, II. Examples in photon correction spectroscopy and Frauenhofer diffraction, Inverse Problems, 7 (1991), 1–20, 21–41. doi: 10.1088/0266-5611/7/1/004.  Google Scholar

[17]

P. L. Butzer and S. Jansche, A direct approach to the Mellin transform, J. Fourier Anal. Appl., 3 (1997), 325-376.  doi: 10.1007/BF02649101.  Google Scholar

[18]

P. L. Butzer and S. Jansche, The exponential sampling theorem of signal analysis, Atti Sem. Mat. Fis. Univ. Modena, Suppl., (special issue dedicated to Professor Calogero Vinti), 46 (1998), 99–122.  Google Scholar

[19]

P. L. Butzer and S. Jansche, A self-contained approach to Mellin transform analysis for square integrable functions; applications, Integral Transform. Spec. Funct., 8 (1999), 175-198.  doi: 10.1080/10652469908819226.  Google Scholar

[20]

P. L. Butzer, G. Schmeisser and R. L. Stens, An introduction to sampling analysis, In: Marvasti, F. (ed. ) Nonuniform Sampling, Theory and Practice, 17–121. Kluwer Academic/Plenum Publishers, New York, (2001).  Google Scholar

[21]

P. L. ButzerW. Splettstöẞer and R. L. Stens, The sampling theorem and linear prediction in signal analysis, Jahresber. Deutsch. Math.-Verein., 90 (1988), 1-70.   Google Scholar

[22]

P. L. Butzer and R. L. Stens, Linear prediction by samples from the past, In: Marks II, R.J. (ed. ) Advanced Topics in Shannon Sampling and Interpolation Theory, 157–183. Springer, New York, (1993).  Google Scholar

[23]

D. Casasent, Optical signal processing, In: Casasent, D. (ed. ) Optical Data Processing, 241–282. Springer, Berlin, (1978). doi: 10.1007/BFb0057988.  Google Scholar

[24]

D. CostarelliA. M. Minotti and G. Vinti, Approximation of discontinuous signals by sampling Kantorovich series, J. Math. Anal. Appl., 450 (2017), 1083-1103.  doi: 10.1016/j.jmaa.2017.01.066.  Google Scholar

[25]

D. Costarelli, M. Piconi and G. Vinti, On the convergence properties of Durrmeyer-Sampling type operators in Orlicz spaces, to appear, arXiv: 2007.02450v1, 2021. Google Scholar

[26]

D. Costarelli, M Seracini and G. Vinti, A comparison between the sampling Kantorovich algorithm for digital image processing with some interpolation and quasi-interpolation methods, Appl. Math. Comput., 347, (2020), 125046, 18 pp. doi: 10.1016/j. amc. 2020.125046.  Google Scholar

[27]

D. CostarelliM. Seracini and G. Vinti, A segmentation procedure of the pervious area of the aorta artery from CT images without contrast medium, Math. Methods Appl. Sci., 43 (2020), 114-133.  doi: 10.1002/mma.5838.  Google Scholar

[28]

D. Costarelli and G. Vinti, An inverse result of approximation by sampling Kantorovich series, Proc. Edinb. Math. Soc., 62 (2019), 265-280.  doi: 10.1017/S0013091518000342.  Google Scholar

[29]

D. Costarelli and G. Vinti, Saturation by the Fourier transform method for the sampling Kantorovich series based on bandlimited kernels, Anal. Math. Phys., 9 (2019), 2263-2280.  doi: 10.1007/s13324-019-00334-6.  Google Scholar

[30] J. R. Higgins, Sampling Theory in Fourier and Signal Analysis, Foundations. Oxford Univ. Press, Oxford, 1996.   Google Scholar
[31]

A. Kivinukk and G. Tamberg, Interpolating generalized Shannon sampling operators, their norms and approximation properties, Sampl. Theory Signal Image Process., 8 (2009), 77-95.  doi: 10.1007/BF03549509.  Google Scholar

[32]

A. Kivinukk and G. Tamberg, On window methods in generalized Shannon sampling operators., In New perspectives on approximation and sampling theory, 63–85, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, Cham, (2014).  Google Scholar

[33]

A. S. Kumar and S. Bajpeyi, Direct and inverse results for Kantorovich type exponential sampling series, Results Math., 75 (2020), Paper No. 119, 17 pp. doi: 10.1007/s00025-020-01241-0.  Google Scholar

[34]

A. S. Kumar and D. Ponnaian, Approximation by generalized bivariate Kantorovich sampling type series, J. Anal., 27 (2019), 429-449.  doi: 10.1007/s41478-018-0085-6.  Google Scholar

[35]

A. S. Kumar and B. Shivam, Inverse approximation and GBS of bivariate Kantorovich type sampling series, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 114 (2020), Paper No. 82, 15 pp. doi: 10.1007/s13398-020-00805-7.  Google Scholar

[36]

N. OstrowskyD. SornetteP. Parker and E. R. Pike, Exponential sampling method for light scattering polydispersity analysis, Opt. Acta, 28 (1981), 1059-1070.  doi: 10.1080/713820704.  Google Scholar

[37]

S. Ries and R. L. Stens, Approximation by generalized sampling series, In: Sendov, Bl., Petrushev, P., Maalev, R., Tashev, S. (eds. )Constructive Theory of Functions, pp. 746–756. Pugl. House Bulgarian Academy of Sciences, Sofia, (1984). Google Scholar

[38]

G. Schmeisser, Interconnections between the multiplier methods and the window methods in generalized sampling, Sampl. Theory Signal Image Process., 9 (2010), 1-24.  doi: 10.1007/BF03549522.  Google Scholar

[39] A. I. Zayed, Advances in Shannon's Sampling Theory, CRC Press, Boca Raton, 1993.   Google Scholar

show all references

References:
[1]

L. AngeloniD. Costarelli and G. Vinti, A characterization of the convergence in variation for the generalized sampling series, Ann. Acad. Sci. Fenn. Math., 43 (2018), 755-767.  doi: 10.5186/aasfm.2018.4343.  Google Scholar

[2]

L. AngeloniD. Costarelli and G. Vinti, Convergence in variation for the multidimensional generalized sampling series and applications to smoothing for digital image processing, Ann. Acad. Sci. Fenn. Math., 45 (2020), 751-770.  doi: 10.5186/aasfm.2020.4532.  Google Scholar

[3]

F. AsdrubaliG. BaldinelliF. BianchiD. CostarelliA. RotiliM. Seracini and G. Vinti, Detection of thermal bridges from thermographic images by means of image processing approximation algorithms, Appl. Math. Comput., 317 (2018), 160-171.  doi: 10.1016/j.amc.2017.08.058.  Google Scholar

[4]

S. Balsamo and I. Mantellini, On linear combinations of general exponential sampling series, Results Math., 74 (2019), Paper No. 180, 19 pp. doi: 10.1007/s00025-019-1104-x.  Google Scholar

[5]

C. BardaroP. L. Butzer and I. Mantellini, The exponential sampling theorem of signal analysis and the reproduction kernel formula in the Mellin transform setting, Sampl. Theory Signal Image Process., 13 (2014), 35-66.  doi: 10.1007/BF03549572.  Google Scholar

[6]

C. BardaroP. L. Butzer and I. Mantellini, The Mellin-Parseval formula and its interconnections with the exponential sampling theorem of optical physics, Integral Transforms and Special Functions, 27 (2016), 17-29.  doi: 10.1080/10652469.2015.1087401.  Google Scholar

[7]

C. BardaroP. L. ButzerR. L. Stens and G. Vinti, Prediction by samples from the past with error estimates covering discontinuous signals, IEEE Trans. Information Theory, 56 (2010), 614-633.  doi: 10.1109/TIT.2009.2034793.  Google Scholar

[8]

C. BardaroL Faina and I. Mantellini, A generalization of the exponential sampling series and its approximation properties, Math. Slovaca., 67 (2017), 1481-1496.  doi: 10.1515/ms-2017-0064.  Google Scholar

[9]

C. BardaroL. Faina and I. Mantellini, Quantitative Voronovskaja formulae for generalized Durrmeyer sampling type series, Math. Nachr., 289 (2016), 1702-1720.  doi: 10.1002/mana.201500225.  Google Scholar

[10]

C. Bardaro and I. Mantellini, A quantitative Voronovskaja formula for generalized sampling operators, East J. Approx., 15 (2009), 459-471.   Google Scholar

[11]

C. Bardaro and I. Mantellini, Asymptotic formulae for linear combinations of generalized sampling type operators, Z. Anal. Anwend., 32 (2013), 279-298.  doi: 10.4171/ZAA/1485.  Google Scholar

[12]

C. Bardaro and I. Mantellini, Asymptotic expansion of generalized Durrmeyer sampling type series, Jaen Journal on Approximation, 6 (2014), 143-165.   Google Scholar

[13]

C. Bardaro and I. Mantellini, On a Durrmeyer type modifcation of the Exponential sampling series, Rend. Circ. Mat. Palermo (2), 70 (2021), 1289-1304.  doi: 10.1007/s12215-020-00559-6.  Google Scholar

[14]

C. Bardaro, I. Mantellini and G. Schmeisser, Exponential sampling series: Convergence in Mellin-Lebesgue spaces, Results Math., 74 (2019), Paper No. 119, 20 pp. doi: 10.1007/s00025-019-1044-5.  Google Scholar

[15]

C. BardaroG. VintiP. L. Butzer and R. L. Stens, Kantorovich-type generalized sampling series in the setting of Orlicz spaces, Sampling Theory Signal Image Processing, 6 (2007), 29-52.  doi: 10.1007/BF03549462.  Google Scholar

[16]

M. Bertero and E. R. Pike, Exponential sampling method for Laplace and other dilationally invariant transforms: I. Singular-system analysis, II. Examples in photon correction spectroscopy and Frauenhofer diffraction, Inverse Problems, 7 (1991), 1–20, 21–41. doi: 10.1088/0266-5611/7/1/004.  Google Scholar

[17]

P. L. Butzer and S. Jansche, A direct approach to the Mellin transform, J. Fourier Anal. Appl., 3 (1997), 325-376.  doi: 10.1007/BF02649101.  Google Scholar

[18]

P. L. Butzer and S. Jansche, The exponential sampling theorem of signal analysis, Atti Sem. Mat. Fis. Univ. Modena, Suppl., (special issue dedicated to Professor Calogero Vinti), 46 (1998), 99–122.  Google Scholar

[19]

P. L. Butzer and S. Jansche, A self-contained approach to Mellin transform analysis for square integrable functions; applications, Integral Transform. Spec. Funct., 8 (1999), 175-198.  doi: 10.1080/10652469908819226.  Google Scholar

[20]

P. L. Butzer, G. Schmeisser and R. L. Stens, An introduction to sampling analysis, In: Marvasti, F. (ed. ) Nonuniform Sampling, Theory and Practice, 17–121. Kluwer Academic/Plenum Publishers, New York, (2001).  Google Scholar

[21]

P. L. ButzerW. Splettstöẞer and R. L. Stens, The sampling theorem and linear prediction in signal analysis, Jahresber. Deutsch. Math.-Verein., 90 (1988), 1-70.   Google Scholar

[22]

P. L. Butzer and R. L. Stens, Linear prediction by samples from the past, In: Marks II, R.J. (ed. ) Advanced Topics in Shannon Sampling and Interpolation Theory, 157–183. Springer, New York, (1993).  Google Scholar

[23]

D. Casasent, Optical signal processing, In: Casasent, D. (ed. ) Optical Data Processing, 241–282. Springer, Berlin, (1978). doi: 10.1007/BFb0057988.  Google Scholar

[24]

D. CostarelliA. M. Minotti and G. Vinti, Approximation of discontinuous signals by sampling Kantorovich series, J. Math. Anal. Appl., 450 (2017), 1083-1103.  doi: 10.1016/j.jmaa.2017.01.066.  Google Scholar

[25]

D. Costarelli, M. Piconi and G. Vinti, On the convergence properties of Durrmeyer-Sampling type operators in Orlicz spaces, to appear, arXiv: 2007.02450v1, 2021. Google Scholar

[26]

D. Costarelli, M Seracini and G. Vinti, A comparison between the sampling Kantorovich algorithm for digital image processing with some interpolation and quasi-interpolation methods, Appl. Math. Comput., 347, (2020), 125046, 18 pp. doi: 10.1016/j. amc. 2020.125046.  Google Scholar

[27]

D. CostarelliM. Seracini and G. Vinti, A segmentation procedure of the pervious area of the aorta artery from CT images without contrast medium, Math. Methods Appl. Sci., 43 (2020), 114-133.  doi: 10.1002/mma.5838.  Google Scholar

[28]

D. Costarelli and G. Vinti, An inverse result of approximation by sampling Kantorovich series, Proc. Edinb. Math. Soc., 62 (2019), 265-280.  doi: 10.1017/S0013091518000342.  Google Scholar

[29]

D. Costarelli and G. Vinti, Saturation by the Fourier transform method for the sampling Kantorovich series based on bandlimited kernels, Anal. Math. Phys., 9 (2019), 2263-2280.  doi: 10.1007/s13324-019-00334-6.  Google Scholar

[30] J. R. Higgins, Sampling Theory in Fourier and Signal Analysis, Foundations. Oxford Univ. Press, Oxford, 1996.   Google Scholar
[31]

A. Kivinukk and G. Tamberg, Interpolating generalized Shannon sampling operators, their norms and approximation properties, Sampl. Theory Signal Image Process., 8 (2009), 77-95.  doi: 10.1007/BF03549509.  Google Scholar

[32]

A. Kivinukk and G. Tamberg, On window methods in generalized Shannon sampling operators., In New perspectives on approximation and sampling theory, 63–85, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, Cham, (2014).  Google Scholar

[33]

A. S. Kumar and S. Bajpeyi, Direct and inverse results for Kantorovich type exponential sampling series, Results Math., 75 (2020), Paper No. 119, 17 pp. doi: 10.1007/s00025-020-01241-0.  Google Scholar

[34]

A. S. Kumar and D. Ponnaian, Approximation by generalized bivariate Kantorovich sampling type series, J. Anal., 27 (2019), 429-449.  doi: 10.1007/s41478-018-0085-6.  Google Scholar

[35]

A. S. Kumar and B. Shivam, Inverse approximation and GBS of bivariate Kantorovich type sampling series, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 114 (2020), Paper No. 82, 15 pp. doi: 10.1007/s13398-020-00805-7.  Google Scholar

[36]

N. OstrowskyD. SornetteP. Parker and E. R. Pike, Exponential sampling method for light scattering polydispersity analysis, Opt. Acta, 28 (1981), 1059-1070.  doi: 10.1080/713820704.  Google Scholar

[37]

S. Ries and R. L. Stens, Approximation by generalized sampling series, In: Sendov, Bl., Petrushev, P., Maalev, R., Tashev, S. (eds. )Constructive Theory of Functions, pp. 746–756. Pugl. House Bulgarian Academy of Sciences, Sofia, (1984). Google Scholar

[38]

G. Schmeisser, Interconnections between the multiplier methods and the window methods in generalized sampling, Sampl. Theory Signal Image Process., 9 (2010), 1-24.  doi: 10.1007/BF03549522.  Google Scholar

[39] A. I. Zayed, Advances in Shannon's Sampling Theory, CRC Press, Boca Raton, 1993.   Google Scholar
[1]

Peng Sun. Exponential decay of Lebesgue numbers. Discrete & Continuous Dynamical Systems, 2012, 32 (10) : 3773-3785. doi: 10.3934/dcds.2012.32.3773

[2]

Ferenc Weisz. Cesàro summability and Lebesgue points of higher dimensional Fourier series. Mathematical Foundations of Computing, 2021  doi: 10.3934/mfc.2021033

[3]

Hongjie Dong, Kunrui Wang. Interior and boundary regularity for the Navier-Stokes equations in the critical Lebesgue spaces. Discrete & Continuous Dynamical Systems, 2020, 40 (9) : 5289-5323. doi: 10.3934/dcds.2020228

[4]

Jie Jiang. Global stability of Keller–Segel systems in critical Lebesgue spaces. Discrete & Continuous Dynamical Systems, 2020, 40 (1) : 609-634. doi: 10.3934/dcds.2020025

[5]

Julii A. Dubinskii. Complex Neumann type boundary problem and decomposition of Lebesgue spaces. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 201-210. doi: 10.3934/dcds.2004.10.201

[6]

Hartmut Pecher. Almost optimal local well-posedness for the Maxwell-Klein-Gordon system with data in Fourier-Lebesgue spaces. Communications on Pure & Applied Analysis, 2020, 19 (6) : 3303-3321. doi: 10.3934/cpaa.2020146

[7]

Adalet Hanachi, Haroune Houamed, Mohamed Zerguine. On the global well-posedness of the axisymmetric viscous Boussinesq system in critical Lebesgue spaces. Discrete & Continuous Dynamical Systems, 2020, 40 (11) : 6473-6506. doi: 10.3934/dcds.2020287

[8]

Andreia Chapouto. A remark on the well-posedness of the modified KdV equation in the Fourier-Lebesgue spaces. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3915-3950. doi: 10.3934/dcds.2021022

[9]

Chao Deng, Tong Li. Global existence and large time behavior of a 2D Keller-Segel system in logarithmic Lebesgue spaces. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 183-195. doi: 10.3934/dcdsb.2018093

[10]

Hartmut Pecher. The Chern-Simons-Higgs and the Chern-Simons-Dirac equations in Fourier-Lebesgue spaces. Discrete & Continuous Dynamical Systems, 2019, 39 (8) : 4875-4893. doi: 10.3934/dcds.2019199

[11]

Xiaoying Han. Exponential attractors for lattice dynamical systems in weighted spaces. Discrete & Continuous Dynamical Systems, 2011, 31 (2) : 445-467. doi: 10.3934/dcds.2011.31.445

[12]

Vyacheslav K. Isaev, Vyacheslav V. Zolotukhin. Introduction to the theory of splines with an optimal mesh. Linear Chebyshev splines and applications. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 471-489. doi: 10.3934/naco.2013.3.471

[13]

Alexandre Nolasco de Carvalho, Stefanie Sonner. Pullback exponential attractors for evolution processes in Banach spaces: Theoretical results. Communications on Pure & Applied Analysis, 2013, 12 (6) : 3047-3071. doi: 10.3934/cpaa.2013.12.3047

[14]

Alexandre Nolasco de Carvalho, Stefanie Sonner. Pullback exponential attractors for evolution processes in Banach spaces: Properties and applications. Communications on Pure & Applied Analysis, 2014, 13 (3) : 1141-1165. doi: 10.3934/cpaa.2014.13.1141

[15]

Cesare Bracco, Annalisa Buffa, Carlotta Giannelli, Rafael Vázquez. Adaptive isogeometric methods with hierarchical splines: An overview. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 241-261. doi: 10.3934/dcds.2019010

[16]

Paula Balseiro, Teresinha J. Stuchi, Alejandro Cabrera, Jair Koiller. About simple variational splines from the Hamiltonian viewpoint. Journal of Geometric Mechanics, 2017, 9 (3) : 257-290. doi: 10.3934/jgm.2017011

[17]

Purshottam Narain Agrawal, Şule Yüksel Güngör, Abhishek Kumar. Better degree of approximation by modified Bernstein-Durrmeyer type operators. Mathematical Foundations of Computing, 2021  doi: 10.3934/mfc.2021024

[18]

Keaton Hamm, Longxiu Huang. Stability of sampling for CUR decompositions. Foundations of Data Science, 2020, 2 (2) : 83-99. doi: 10.3934/fods.2020006

[19]

Éder Rítis Aragão Costa. An extension of the concept of exponential dichotomy in Fréchet spaces which is stable under perturbation. Communications on Pure & Applied Analysis, 2019, 18 (2) : 845-868. doi: 10.3934/cpaa.2019041

[20]

Tomás Caraballo, Stefanie Sonner. Random pullback exponential attractors: General existence results for random dynamical systems in Banach spaces. Discrete & Continuous Dynamical Systems, 2017, 37 (12) : 6383-6403. doi: 10.3934/dcds.2017277

 Impact Factor: 

Article outline

[Back to Top]