Convergence and rate of approximation for linear integral operators in BVφ-spaces in multidimensional setting

被引：36

作者：

Angeloni, Laura ^{[1
]}

Vinti, Gianluca ^{[1
]}

机构：

[1] Univ Perugia, Dipartimento Matemat & Informat, I-06123 Perugia, Italy

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 349卷 / 02期

关键词：

Linear convolution integral operators; Multidimensional phi-variation; Rate of approximation; Lipschitz classes; phi-modulus of smoothness; Higher order of approximation; GENERALIZED VARIATION;

D O I：

10.1016/j.jmaa.2008.08.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper. where for the first time it is introduced a multidimensional concept of phi-variation in the sense of Tonelli, we extend previous results concerning convergence, order of approximation and higher order of approximation for linear integral operators in BV phi(R-N) (space of functions with bounded phi-variation in R-N). Moreover we give a further generalization of the theory introducing the concept of F-phi-variation, where F is a continuous sublinear functional. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：317 / 334

页数：18

共 38 条

[11]

Boni M., 1971, ATTI SEMINARIO MATEM, V20, P187

[12]

Butzer P.L., 1971, Reviews in Group Representation Theory, Part A (Pure and Applied Mathematics Series, V1

[13]

Camille J., 1881, Camptesrendushebdomadaires Sances Lacademie Des Sci, V92, P228, DOI [10.2307/2316319 (French, DOI 10.2307/2316319(FRENCH]

[14]

De Giorgi E., 1954, Ann. Mat. Pura Appl. (4), V36, P191, DOI [10.1007/BF02412838, DOI 10.1007/BF02412838]