Approximation in variation by homothetic operators in multidimensional setting

Differential and Integral Equations

Volumn 26, Issue 5-6, 2013, Pages 655-674

  Angeloni, Laura ^a   Vinti, Gianluca ^a  

^a UNIVERSITY OF PERUGIA   (Italy)

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EID: 84886484681     PISSN: 08934983     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (49)

1. L. Angeloni, A characterization of a modulus of smoothness in multidimensional setting, Boll. Unione Mat. Ital., Serie IX, 4 (2011), 79-108.
2. L. Angeloni, Convergence in variation for a homothetic modulus of smoothness in multidimensional setting, Comm. Appl. Nonlinear Anal., 19 (2012), 1-22.
3. L. Angeloni, Approximation results with respect to multidimensional '-variation for nonlinear integral operators, Z. Anal. Anwendungen, 32 (2013), 103-128.
4. L. Angeloni and G. Vinti, A unied approach to approximation results with applications to nonlinear sampling theory, Int. Journal of Math. Sciences, 3 (2004), 95-130.
5. L. Angeloni and G. Vinti, Rate of approximation for nonlinear integral operators with application to signal processing, Differential Integral Equations, 18 (2005), 855-890.
6. L. Angeloni and G. Vinti, Convergence in variation and rate of approximation for nonlinear integral operators of convolution type, Results Math., 49 (2006), 1-23
7. Erratum: 57 (2010), 387-391.
8. L. Angeloni and G. Vinti, Approximation by means of nonlinear integral operators in the space of functions with bounded '-variation, Differential Integral Equations, 20 (2007), 339-360
9. L. Angeloni and G. Vinti, Convergence and rate of approximation for linear integral operators in BV '-spaces in multidimensional setting, J. Math. Anal. Appl., 349 (2009), 317-334.
10. L. Angeloni and G. Vinti, Approximation with respect to Goffman-Serrin variation by means of non-convolution type integral operators, Numer. Funct. Anal. Optim., 31 (2010), 519-548.
11. L. Angeloni and G. Vinti, A sufficient Condition for the convergence of a certain modulus of smoothness in multidimensional setting, Comm. Appl. Nonlinear Anal., 20 (2013), 1-20.
12. C. Bardaro, P.L. Butzer, R.L. Stens, and G. Vinti, Convergence in variation and rates of approximation for Bernstein-type polynomials and singular convolution integrals, Analysis, 23 (2003), 299-340.
13. C. Bardaro, J. Musielak, and G. Vinti, "Nonlinear Integral Operators and Applications," De Gruyter Series in Nonlinear Analysis and Applications, New York, Berlin, 9, 2003.
14. C. Bardaro, S. Sciamannini, and G. Vinti, Convergence in BV' by nonlinear Mellintype convolution operators, Funct. Approx. Comment. Math., 29 (2001), 17-28.
15. C. Bardaro and G. Vinti, Integral operators on vector measures and applications to the moment kernel, Rend. Mat. Appl., 8 (1988), 149-164.
16. C. Bardaro and G. Vinti, Modular convergence in generalized Orlicz spaces for moment type operators, Appl. Anal., 32 (1989), 265-276.
17. C. Bardaro and G. Vinti, On convergence of moment operators with respect to '- variation, Appl. Anal., 41 (1991), 247-256.
18. C. Bardaro and G. Vinti, Some estimates of integral operators with respect to the multidimensional Vitali '-variation and applications in fractional calculus, Rend. Mat. Appl., Serie VII, 11 (1991), 405-416.
19. C. Bardaro and G. Vinti, A general convergence theorem with respect to Cesari variation and applications, Nonlinear Anal., 22 (1994), 505-518.
20. C. Bardaro and G. Vinti, Some inclusion theorems for Orlicz and Musielak-Orlicz type spaces, Ann. Mat. Pura Appl., 68 (1995), 189-203.
21. C. Bardaro and G. Vinti, A general approach to the convergence theorems of generalized sampling series, Appl. Anal., 64 (1997), 203-217.
22. C. Bardaro and G. Vinti, On the order of BV'-approximation of convolution integrals over the line group, Comment. Math. Prace Mat., Tomus Specialis in Honorem Iuliani Musielak (2004), 47-63.
23. C. Bardaro and G. Vinti, Approximation of multivariate functions of bounded variation by means of linear convolution operators, Varahmihir J. Math. Sci., 6 (2006), 393-404.
24. P.L. Butzer and R.J. Nessel, "Fourier Analysis and Approximation, I," Academic Press, New York-London, 1971.
25. L. Cesari, Sulle funzioni a variazione limitata, Ann. Sc. Norm. Super. Pisa, 5 (1936), 299-313.
26. V.V. Chistyakov and O.E. Galkin, Mappings of bounded-variation with arbitrary function, J. Dynam. Control Systems, 4 (1998), 217-247.
27. E. De Giorgi, Su una teoria generale della misura (r 1)-dimensionale in uno spazio ad r dimensioni, Ann. Mat. Pura Appl., 36 (1954), 191-213.
28. E. Giusti, "Minimal Surfaces and Functions of Bounded Variation," Monographs in Mathematics, vol. 80, Birkhlauser Verlag, Basel, 1984.
29. H.H. Herda, Modular spaces of generalized variation, Studia Math., 30 (1968), 21-42.
30. E.R. Love and L.C. Young, Sur une classe de fonctionnelles lineaires, Fund. Math., 28 (1937), 243-257.
31. L. Maligranda and W. Orlicz, On some properties of functions of generalized variation, Mh. Math., 104 (1987), 53-65.
32. I. Mantellini and G. Vinti, φ;-variation and nonlinear integral operators, Atti Sem. Mat. Fis. Univ. Modena, Suppl. Vol. 46, a special issue of the International Conference in Honour of Prof. Calogero Vinti (1998), 847-862.
33. W. Matuszewska and W. Orlicz, On property B1 for functions of bounded 'φvariation, Bull. Polish Acad. Sci. Math., 35 (1987), 57-69.
34. J. Musielak, "Orlicz Spaces and Modular Spaces," Springer-Verlag, Lecture Notes in Math., 1034, 1983.
35. J. Musielak, Nonlinear approximation in some modular function spaces I, Math. Japon., 38 (1993), 83-90.
36. J. Musielak and W. Orlicz, On generalized variations (I), Studia Math., 18 (1959), 11-41.
37. T. Radó, "Length and Area," Amer. Math. Soc. Colloquium Publications, 30, 1948.
38. A.R.K. Ramazanov, On approximation of functions in terms of φ-variation, Anal. Math., 20 (1994), 263-281.
39. S. Sciamannini and G. Vinti, Convergence and rate of approximation in BV' for a class of integral operators, Approx. Theory Appl., 17 (2001), 17-35.
40. S. Sciamannini and G. Vinti, Convergence results in BV' for a class of nonlinear Volterra-Hammerstein integral operators and applications, J. Concrete Appl. Anal., 1 (2003), 287-306.
41. J. Szelmeczka, On convergence of singular integrals in the generalized variation metric, Funct. Approx. Comment. Math., 15 (1986), 53-58.
42. L. Tonelli, Su alcuni concetti dell'analisi moderna, Ann. Sc. Norm. Super. Pisa, 11 (1942), 107-118.
43. C. Vinti, Perimetro variazione, Ann. Sc. Norm. Super. Pisa, 18 (1964), 201-231.
44. G. Vinti, The generalized '-variation in the sense of Vitali: Estimates for integral operators and applications in fractional calculus, Comment. Math. Prace Mat., 34 (1994), 199-213.
45. G. Vinti, A general approximation result for nonlinear integral operators and applications to signal processing, Appl. Anal., 79 (2001), 217-238.
46. G. Vinti, Approximation in Orlicz spaces for linear integral operators and applications, Rend. Circ. Mat. Palermo, Serie II, Suppl., 76 (2005), 103-127.
47. N. Wiener, The quadratic variation of a function and its Fourier coeficients, Massachusetts J. of Math., 3 (1924), 72-94.
48. L.C. Young, An inequality of the Hölder type, connected with Stieltjes integration, Acta Math., 67 (1936), 251-282.
49. L.C. Young, General inequalities for Stieltjes integrals and the convergence of Fourier series, Math. Ann., 115 (1938), 581-612.