Approximation on variable exponent spaces by linear integral operators
This paper aims at approximation of functions by linear integral operators on variable exponent spaces associated with a general exponent function on a domain of a Euclidean space. Under a log-Hölder continuity assumption of the exponent function, we present quantitative estimates for the approximat...
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| Vydané v: | Journal of approximation theory Ročník 223; s. 29 - 51 |
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| Abstract | This paper aims at approximation of functions by linear integral operators on variable exponent spaces associated with a general exponent function on a domain of a Euclidean space. Under a log-Hölder continuity assumption of the exponent function, we present quantitative estimates for the approximation and solve an open problem raised in our earlier work. As applications of our key estimates, we provide high orders of approximation by quasi-interpolation type and linear combinations of Bernstein type integral operators on variable exponent spaces. We also introduce K-functionals and moduli of smoothness on variable exponent spaces and discuss their relationships and applications. |
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| AbstractList | This paper aims at approximation of functions by linear integral operators on variable exponent spaces associated with a general exponent function on a domain of a Euclidean space. Under a log-Hölder continuity assumption of the exponent function, we present quantitative estimates for the approximation and solve an open problem raised in our earlier work. As applications of our key estimates, we provide high orders of approximation by quasi-interpolation type and linear combinations of Bernstein type integral operators on variable exponent spaces. We also introduce K-functionals and moduli of smoothness on variable exponent spaces and discuss their relationships and applications. |
| Author | He, Bo-Lu Zhou, Ding-Xuan Li, Bing-Zheng |
| Author_xml | – sequence: 1 givenname: Bing-Zheng surname: Li fullname: Li, Bing-Zheng email: libingzheng@zju.edu.cn organization: Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China – sequence: 2 givenname: Bo-Lu surname: He fullname: He, Bo-Lu organization: Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China – sequence: 3 givenname: Ding-Xuan orcidid: 0000-0003-0224-9216 surname: Zhou fullname: Zhou, Ding-Xuan email: mazhou@cityu.edu.hk organization: Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong |
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| Cites_doi | 10.1016/j.acha.2011.01.001 10.1512/iumj.1972.21.21054 10.1016/j.jat.2013.04.007 10.1006/jmaa.1994.1229 10.1214/aos/1079120131 10.1007/s10444-008-9082-7 10.1002/mana.200410479 10.1016/j.jmaa.2012.03.004 10.1142/S0219530514500110 10.1002/sapm1969483265 10.1090/S0025-5718-1987-0878701-2 10.1006/jmaa.2000.7617 10.1016/j.jat.2009.11.005 10.1109/ICIP.1997.632128 10.1090/S0002-9939-1987-0877032-6 10.1137/050624522 10.1007/s002050100117 10.1155/2014/454375 10.1137/S0036141095279869 10.3150/10-BEJ267 10.1016/j.acha.2014.12.005 10.1090/S0002-9939-1985-0810161-X 10.1142/S0219530517500026 10.1007/BF01904041 10.4064/sm-3-1-200-211 10.1016/j.jco.2008.07.001 10.1016/0021-9045(85)90043-7 10.1007/BF01208430 10.1007/s10444-004-7206-2 |
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| Keywords | Integral operators 41A36 log-Hölder continuity 68T05 K-functional Variable exponent space Bernstein type operators Learning theory 68Q32 |
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| References | Li, Zhou (b32) 2014; 2014 Derriennic (b17) 1985; 45 Ditzian, Totik (b19) 1987; vol. 9 Orlicz (b35) 1931; 3 de Boor, Höllig, Riemenschneider (b11) 1985; 29 Diening, Harjulehto, Hästö, Ružička (b18) 2011 Durrmeyer (b20) 1967 de Boor, Jia (b12) 1985; 95 Lei, Jia, Cheney (b30) 1997; 28 Acerbi, Mingione (b1) 2001; 156 Hu, Fan, Wu, Zhou (b25) 2015; 13 Bollt, Chartrand, Esedoglu, Schultz, Vixie (b9) 2009; 31 Chui, Jetter, Ward (b15) 1987; 48 Cruz-Uribe, SFO, Fiorenza (b16) 2007; 280 Fan, Hu, Wu, Zhou (b21) 2016; 41 Fan, Zhao (b22) 2001; 263 Kantorovich (b27) 1930 Chui, Diamond (b14) 1987; 99 Zhou, Jetter (b43) 2006; 25 P. Blomgren, T. Chan, P. Mulet, C.K. Wong, Total variation image restoration: numerical methods and extensions, in: Proceedings of the 1997 IEEE International Conference on Image Processing, vol. III, 1997, pp. 384–387. Fix, Strang (b23) 1969; 48 Shi, Feng, Zhou (b37) 2011; 31 Bernstein (b7) 1912–1913; 13 Stein (b38) 1970 Kovácik, Rákosnk (b28) 1991; 41 Zhou (b41) 1993; 19 Berens, Lorentz (b5) 1972; 21 Zhou (b42) 2014; 9 Pan, Xiang, Xiao, Zhou (b36) 2008; 24 Steinwart, Christman (b39) 2011; 17 Guo, Xiang, Guo, Zhou (b24) 2017; 15 Berdysheva (b2) 2012; 394 Lei (b29) 1994; 185 Mallat (b33) 1989; 315 Meyer (b34) 1990 Jetter, Zhou (b26) 1995; 11 Chen, Levine, Rao (b13) 2006; 66 Berens, Xu (b6) 1991 de Boor, DeVore, Ron (b10) 1994; 341 Tsybakov (b40) 2004; 32 Berens, DeVore (b4) 1978; 245 Berdysheva, Jetter (b3) 2010; 162 Li (b31) 2013; 173 Lei (10.1016/j.jat.2017.07.009_b29) 1994; 185 Hu (10.1016/j.jat.2017.07.009_b25) 2015; 13 Li (10.1016/j.jat.2017.07.009_b31) 2013; 173 Cruz-Uribe (10.1016/j.jat.2017.07.009_b16) 2007; 280 Berens (10.1016/j.jat.2017.07.009_b5) 1972; 21 Durrmeyer (10.1016/j.jat.2017.07.009_b20) 1967 Zhou (10.1016/j.jat.2017.07.009_b42) 2014; 9 Jetter (10.1016/j.jat.2017.07.009_b26) 1995; 11 Berdysheva (10.1016/j.jat.2017.07.009_b2) 2012; 394 Meyer (10.1016/j.jat.2017.07.009_b34) 1990 Bollt (10.1016/j.jat.2017.07.009_b9) 2009; 31 Acerbi (10.1016/j.jat.2017.07.009_b1) 2001; 156 10.1016/j.jat.2017.07.009_b8 Pan (10.1016/j.jat.2017.07.009_b36) 2008; 24 Berens (10.1016/j.jat.2017.07.009_b4) 1978; 245 Shi (10.1016/j.jat.2017.07.009_b37) 2011; 31 Diening (10.1016/j.jat.2017.07.009_b18) 2011 Bernstein (10.1016/j.jat.2017.07.009_b7) 1912; 13 Li (10.1016/j.jat.2017.07.009_b32) 2014; 2014 Stein (10.1016/j.jat.2017.07.009_b38) 1970 Steinwart (10.1016/j.jat.2017.07.009_b39) 2011; 17 Zhou (10.1016/j.jat.2017.07.009_b41) 1993; 19 Zhou (10.1016/j.jat.2017.07.009_b43) 2006; 25 Chen (10.1016/j.jat.2017.07.009_b13) 2006; 66 de Boor (10.1016/j.jat.2017.07.009_b12) 1985; 95 Berens (10.1016/j.jat.2017.07.009_b6) 1991 Chui (10.1016/j.jat.2017.07.009_b15) 1987; 48 de Boor (10.1016/j.jat.2017.07.009_b10) 1994; 341 Fan (10.1016/j.jat.2017.07.009_b22) 2001; 263 Orlicz (10.1016/j.jat.2017.07.009_b35) 1931; 3 Guo (10.1016/j.jat.2017.07.009_b24) 2017; 15 Tsybakov (10.1016/j.jat.2017.07.009_b40) 2004; 32 de Boor (10.1016/j.jat.2017.07.009_b11) 1985; 29 Berdysheva (10.1016/j.jat.2017.07.009_b3) 2010; 162 Fix (10.1016/j.jat.2017.07.009_b23) 1969; 48 Ditzian (10.1016/j.jat.2017.07.009_b19) 1987; vol. 9 Fan (10.1016/j.jat.2017.07.009_b21) 2016; 41 Derriennic (10.1016/j.jat.2017.07.009_b17) 1985; 45 Kantorovich (10.1016/j.jat.2017.07.009_b27) 1930 Lei (10.1016/j.jat.2017.07.009_b30) 1997; 28 Kovácik (10.1016/j.jat.2017.07.009_b28) 1991; 41 Mallat (10.1016/j.jat.2017.07.009_b33) 1989; 315 Chui (10.1016/j.jat.2017.07.009_b14) 1987; 99 |
| References_xml | – volume: vol. 9 year: 1987 ident: b19 publication-title: Moduli of Smoothness – year: 1970 ident: b38 publication-title: Singular Integrals and Differentiability Properties of Functions – volume: 95 start-page: 547 year: 1985 end-page: 553 ident: b12 article-title: Controlled approximation and a characterization of the local approximation order publication-title: Proc. Amer. Math. Soc. – volume: 31 start-page: 61 year: 2009 end-page: 85 ident: b9 article-title: Graduated adaptive image denoising: local compromise between total variation and isotropic diffusion publication-title: Adv. Comput. Math. – volume: 263 start-page: 424 year: 2001 end-page: 446 ident: b22 article-title: On the spaces publication-title: J. Math. Anal. Appl. – volume: 32 start-page: 135 year: 2004 end-page: 166 ident: b40 article-title: Optimal aggregation of classifiers in statistical learning publication-title: Ann. Statist. – volume: 19 start-page: 85 year: 1993 end-page: 100 ident: b41 article-title: Converse theorems for multidimensional Kantorovich operators publication-title: Anal. Math. – start-page: 25 year: 1991 end-page: 46 ident: b6 article-title: On Bernstein-Durrmeyer polynomials with Jacobi weights publication-title: Approximation Theory and Functional Analysis – reference: P. Blomgren, T. Chan, P. Mulet, C.K. Wong, Total variation image restoration: numerical methods and extensions, in: Proceedings of the 1997 IEEE International Conference on Image Processing, vol. III, 1997, pp. 384–387. – year: 1967 ident: b20 article-title: Une formule d’inversion de la transformée Laplace: Applications á la théorie des moments publication-title: Fac. Sci. L’Univ. Paris – volume: 2014 year: 2014 ident: b32 article-title: Analysis of approximation by linear operators on variable publication-title: Abstr. Appl. Anal. – volume: 31 start-page: 286 year: 2011 end-page: 302 ident: b37 article-title: Concentration estimates for learning with publication-title: Appl. Comput. Harmon. Anal. – volume: 66 start-page: 1383 year: 2006 end-page: 1406 ident: b13 article-title: Variable exponent, linear growth functionals in image restoration publication-title: SIAM J. Appl. Math. – volume: 17 start-page: 211 year: 2011 end-page: 225 ident: b39 article-title: Estimating conditional quantiles with the help of the pinball loss publication-title: Bernoulli – volume: 245 start-page: 349 year: 1978 end-page: 361 ident: b4 article-title: Quantitative Korovkin theorems for positive linear operators on Lp spaces publication-title: Trans. Amer. Math. Soc. – year: 1990 ident: b34 publication-title: Ondelettes et Operateurs – start-page: 563 year: 1930 end-page: 568; 595–600 ident: b27 article-title: Sur certaines developments suivant les polynômes de la forme de S. Bernstein I-II publication-title: C. R Acad. Sci. USSR A – volume: 48 start-page: 265 year: 1969 end-page: 273 ident: b23 article-title: Fourier analysis of the finite element method in Ritz-Galerkin theory publication-title: Stud. Appl. Math. – volume: 185 start-page: 1 year: 1994 end-page: 14 ident: b29 article-title: -approximation by cerntain projection operators publication-title: J. Math. Anal. Appl. – volume: 21 start-page: 693 year: 1972 end-page: 708 ident: b5 article-title: Inverse theorems for Bernstein polynomials publication-title: Indiana Univ. Math. J. – volume: 9 start-page: 379 year: 2014 end-page: 391 ident: b42 article-title: Approximation by positive linear operators on variables publication-title: J. Appl. Funct. Anal. – volume: 99 start-page: 643 year: 1987 end-page: 646 ident: b14 article-title: A natural formulation of quasi-interpolation by multivariate spline publication-title: Proc. Amer. Math. Soc. – volume: 48 start-page: 711 year: 1987 end-page: 724 ident: b15 article-title: Cardinal interpolation by multivariate spline publication-title: Math. Comp. – volume: 3 start-page: 200 year: 1931 end-page: 211 ident: b35 article-title: Über konjugierte exponentenfolgen publication-title: Studia Math. – year: 2011 ident: b18 publication-title: Lebesgue and Sobolev Spaces with Variable Exponents – volume: 15 start-page: 433 year: 2017 end-page: 455 ident: b24 article-title: Thresholded spectral algorithms for sparse approximations publication-title: Anal. Appl. – volume: 41 start-page: 592 year: 1991 end-page: 618 ident: b28 article-title: On spaces publication-title: Czechoslovak Math. J. – volume: 11 start-page: 423 year: 1995 end-page: 438 ident: b26 article-title: Order of linear approximation from shift-invariant spaces publication-title: Constr. Approx. – volume: 25 start-page: 323 year: 2006 end-page: 344 ident: b43 article-title: Approximation with polynomial kernels and SVM classifiers publication-title: Adv. Comput. Math. – volume: 13 start-page: 1 year: 1912–1913 end-page: 2 ident: b7 article-title: Démonstration du téoréme de Weierstrass fondée sur le calcul des probabilités publication-title: Commun. Soc. Math. Kharkow – volume: 280 start-page: 256 year: 2007 end-page: 270 ident: b16 article-title: Approximate identities in variable publication-title: Math. Nachr. – volume: 341 start-page: 787 year: 1994 end-page: 806 ident: b10 article-title: Approximation from shift-invariant subspaces of publication-title: Trans. Amer. Math. Soc. – volume: 24 start-page: 606 year: 2008 end-page: 618 ident: b36 article-title: Parzen windows for multi-class classification publication-title: J. Complexity – volume: 28 start-page: 481 year: 1997 end-page: 498 ident: b30 article-title: Approximation from shift-invariant spaces by integral operators publication-title: SIAM J. Math. Anal. – volume: 162 start-page: 576 year: 2010 end-page: 598 ident: b3 article-title: Multivariate Bernstein-Durrmeyer operators with arbitrary weight functions publication-title: J. Approx. Theory – volume: 41 start-page: 164 year: 2016 end-page: 189 ident: b21 article-title: Consistency analysis of an empirical minimum error entropy algorithm publication-title: Appl. Comput. Harmon. Anal. – volume: 45 start-page: 155 year: 1985 end-page: 166 ident: b17 article-title: On multivariate approximation by Bernstein-type polynomials publication-title: J. Approx. Theory – volume: 315 start-page: 69 year: 1989 end-page: 87 ident: b33 article-title: Multiresolution approximations and wavelet orthonormal bases of publication-title: Trans. Amer. Math. Soc. – volume: 156 start-page: 121 year: 2001 end-page: 140 ident: b1 article-title: Regularity results for a class of functionals with nonstandard growth publication-title: Arch. Ration. Mech. Anal. – volume: 394 start-page: 324 year: 2012 end-page: 336 ident: b2 article-title: Uniform convergence of Bernstein-Durrmeyer operators with respect to arbitrary measure publication-title: J. Math. Anal. Appl. – volume: 173 start-page: 33 year: 2013 end-page: 55 ident: b31 article-title: Approximation by multivariate Bernstein-Durrmeyer operators and learning rates of least-square regularized regression with multivariate polynomial kernels publication-title: J. Approx. Theory – volume: 13 start-page: 437 year: 2015 end-page: 455 ident: b25 article-title: Regularization schemes for minimum error entropy principle publication-title: Anal. Appl. – volume: 29 start-page: 533 year: 1985 end-page: 566 ident: b11 article-title: Bivariate cardinal interpolation by spines on a three-direction mesh publication-title: Illinois J. Math. – volume: 31 start-page: 286 year: 2011 ident: 10.1016/j.jat.2017.07.009_b37 article-title: Concentration estimates for learning with ℓ1-regularizer and data dependent hypothesis spaces publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2011.01.001 – volume: 21 start-page: 693 year: 1972 ident: 10.1016/j.jat.2017.07.009_b5 article-title: Inverse theorems for Bernstein polynomials publication-title: Indiana Univ. Math. J. doi: 10.1512/iumj.1972.21.21054 – volume: 173 start-page: 33 year: 2013 ident: 10.1016/j.jat.2017.07.009_b31 article-title: Approximation by multivariate Bernstein-Durrmeyer operators and learning rates of least-square regularized regression with multivariate polynomial kernels publication-title: J. Approx. Theory doi: 10.1016/j.jat.2013.04.007 – volume: 185 start-page: 1 year: 1994 ident: 10.1016/j.jat.2017.07.009_b29 article-title: Lp(Rd)-approximation by cerntain projection operators publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.1994.1229 – year: 1990 ident: 10.1016/j.jat.2017.07.009_b34 – volume: 13 start-page: 1 year: 1912 ident: 10.1016/j.jat.2017.07.009_b7 article-title: Démonstration du téoréme de Weierstrass fondée sur le calcul des probabilités publication-title: Commun. Soc. Math. Kharkow – volume: 32 start-page: 135 year: 2004 ident: 10.1016/j.jat.2017.07.009_b40 article-title: Optimal aggregation of classifiers in statistical learning publication-title: Ann. Statist. doi: 10.1214/aos/1079120131 – volume: 31 start-page: 61 year: 2009 ident: 10.1016/j.jat.2017.07.009_b9 article-title: Graduated adaptive image denoising: local compromise between total variation and isotropic diffusion publication-title: Adv. Comput. Math. doi: 10.1007/s10444-008-9082-7 – volume: 280 start-page: 256 year: 2007 ident: 10.1016/j.jat.2017.07.009_b16 article-title: Approximate identities in variable Lp spaces publication-title: Math. Nachr. doi: 10.1002/mana.200410479 – volume: 394 start-page: 324 year: 2012 ident: 10.1016/j.jat.2017.07.009_b2 article-title: Uniform convergence of Bernstein-Durrmeyer operators with respect to arbitrary measure publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2012.03.004 – volume: 41 start-page: 592 issue: 116 year: 1991 ident: 10.1016/j.jat.2017.07.009_b28 article-title: On spaces Lp(x) and W1,p(x) publication-title: Czechoslovak Math. J. – start-page: 563 year: 1930 ident: 10.1016/j.jat.2017.07.009_b27 article-title: Sur certaines developments suivant les polynômes de la forme de S. Bernstein I-II publication-title: C. R Acad. Sci. USSR A – volume: 13 start-page: 437 year: 2015 ident: 10.1016/j.jat.2017.07.009_b25 article-title: Regularization schemes for minimum error entropy principle publication-title: Anal. Appl. doi: 10.1142/S0219530514500110 – volume: 48 start-page: 265 year: 1969 ident: 10.1016/j.jat.2017.07.009_b23 article-title: Fourier analysis of the finite element method in Ritz-Galerkin theory publication-title: Stud. Appl. Math. doi: 10.1002/sapm1969483265 – volume: 48 start-page: 711 year: 1987 ident: 10.1016/j.jat.2017.07.009_b15 article-title: Cardinal interpolation by multivariate spline publication-title: Math. Comp. doi: 10.1090/S0025-5718-1987-0878701-2 – volume: 263 start-page: 424 year: 2001 ident: 10.1016/j.jat.2017.07.009_b22 article-title: On the spaces Lp(x)(Ω) and Wm,p(x)(Ω) publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.2000.7617 – volume: 162 start-page: 576 year: 2010 ident: 10.1016/j.jat.2017.07.009_b3 article-title: Multivariate Bernstein-Durrmeyer operators with arbitrary weight functions publication-title: J. Approx. Theory doi: 10.1016/j.jat.2009.11.005 – ident: 10.1016/j.jat.2017.07.009_b8 doi: 10.1109/ICIP.1997.632128 – volume: 99 start-page: 643 year: 1987 ident: 10.1016/j.jat.2017.07.009_b14 article-title: A natural formulation of quasi-interpolation by multivariate spline publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-1987-0877032-6 – volume: 66 start-page: 1383 year: 2006 ident: 10.1016/j.jat.2017.07.009_b13 article-title: Variable exponent, linear growth functionals in image restoration publication-title: SIAM J. Appl. Math. doi: 10.1137/050624522 – volume: 156 start-page: 121 year: 2001 ident: 10.1016/j.jat.2017.07.009_b1 article-title: Regularity results for a class of functionals with nonstandard growth publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s002050100117 – start-page: 25 year: 1991 ident: 10.1016/j.jat.2017.07.009_b6 article-title: On Bernstein-Durrmeyer polynomials with Jacobi weights – volume: vol. 9 year: 1987 ident: 10.1016/j.jat.2017.07.009_b19 – volume: 2014 year: 2014 ident: 10.1016/j.jat.2017.07.009_b32 article-title: Analysis of approximation by linear operators on variable Lρp(⋅) spaces and applications in learning theory publication-title: Abstr. Appl. Anal. doi: 10.1155/2014/454375 – volume: 28 start-page: 481 year: 1997 ident: 10.1016/j.jat.2017.07.009_b30 article-title: Approximation from shift-invariant spaces by integral operators publication-title: SIAM J. Math. Anal. doi: 10.1137/S0036141095279869 – volume: 17 start-page: 211 year: 2011 ident: 10.1016/j.jat.2017.07.009_b39 article-title: Estimating conditional quantiles with the help of the pinball loss publication-title: Bernoulli doi: 10.3150/10-BEJ267 – volume: 41 start-page: 164 year: 2016 ident: 10.1016/j.jat.2017.07.009_b21 article-title: Consistency analysis of an empirical minimum error entropy algorithm publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2014.12.005 – volume: 95 start-page: 547 year: 1985 ident: 10.1016/j.jat.2017.07.009_b12 article-title: Controlled approximation and a characterization of the local approximation order publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-1985-0810161-X – volume: 9 start-page: 379 year: 2014 ident: 10.1016/j.jat.2017.07.009_b42 article-title: Approximation by positive linear operators on variables Lp(⋅) space publication-title: J. Appl. Funct. Anal. – volume: 15 start-page: 433 year: 2017 ident: 10.1016/j.jat.2017.07.009_b24 article-title: Thresholded spectral algorithms for sparse approximations publication-title: Anal. Appl. doi: 10.1142/S0219530517500026 – volume: 19 start-page: 85 year: 1993 ident: 10.1016/j.jat.2017.07.009_b41 article-title: Converse theorems for multidimensional Kantorovich operators publication-title: Anal. Math. doi: 10.1007/BF01904041 – year: 2011 ident: 10.1016/j.jat.2017.07.009_b18 – volume: 3 start-page: 200 year: 1931 ident: 10.1016/j.jat.2017.07.009_b35 article-title: Über konjugierte exponentenfolgen publication-title: Studia Math. doi: 10.4064/sm-3-1-200-211 – volume: 315 start-page: 69 year: 1989 ident: 10.1016/j.jat.2017.07.009_b33 article-title: Multiresolution approximations and wavelet orthonormal bases of L2(R) publication-title: Trans. Amer. Math. Soc. – year: 1970 ident: 10.1016/j.jat.2017.07.009_b38 – volume: 24 start-page: 606 year: 2008 ident: 10.1016/j.jat.2017.07.009_b36 article-title: Parzen windows for multi-class classification publication-title: J. Complexity doi: 10.1016/j.jco.2008.07.001 – volume: 245 start-page: 349 year: 1978 ident: 10.1016/j.jat.2017.07.009_b4 article-title: Quantitative Korovkin theorems for positive linear operators on Lp spaces publication-title: Trans. Amer. Math. Soc. – volume: 29 start-page: 533 year: 1985 ident: 10.1016/j.jat.2017.07.009_b11 article-title: Bivariate cardinal interpolation by spines on a three-direction mesh publication-title: Illinois J. Math. – year: 1967 ident: 10.1016/j.jat.2017.07.009_b20 article-title: Une formule d’inversion de la transformée Laplace: Applications á la théorie des moments publication-title: Fac. Sci. L’Univ. Paris – volume: 45 start-page: 155 year: 1985 ident: 10.1016/j.jat.2017.07.009_b17 article-title: On multivariate approximation by Bernstein-type polynomials publication-title: J. Approx. Theory doi: 10.1016/0021-9045(85)90043-7 – volume: 341 start-page: 787 year: 1994 ident: 10.1016/j.jat.2017.07.009_b10 article-title: Approximation from shift-invariant subspaces of L2(Rd) publication-title: Trans. Amer. Math. Soc. – volume: 11 start-page: 423 year: 1995 ident: 10.1016/j.jat.2017.07.009_b26 article-title: Order of linear approximation from shift-invariant spaces publication-title: Constr. Approx. doi: 10.1007/BF01208430 – volume: 25 start-page: 323 year: 2006 ident: 10.1016/j.jat.2017.07.009_b43 article-title: Approximation with polynomial kernels and SVM classifiers publication-title: Adv. Comput. Math. doi: 10.1007/s10444-004-7206-2 |
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| SubjectTerms | [formula omitted]-functional Bernstein type operators Integral operators Learning theory log-Hölder continuity Variable exponent space |
| Title | Approximation on variable exponent spaces by linear integral operators |
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