A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation
We present a review on recent approximation results in the space of functions of bounded variation for some classes of integral operators in the multidimensional setting. In particular, we present estimates and convergence in variation results for both convolution and Mellin integral operators with...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/3843921 |
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| _version_ | 1832566828421873664 |
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| author | Laura Angeloni Gianluca Vinti |
| author_facet | Laura Angeloni Gianluca Vinti |
| author_sort | Laura Angeloni |
| collection | DOAJ |
| description | We present a review on recent approximation results in the space of functions of bounded variation for some classes of integral operators in the multidimensional setting. In particular, we present estimates and convergence in variation results for both convolution and Mellin integral operators with respect to the Tonelli variation. Results with respect to a multidimensional concept of φ-variation in the sense of Tonelli are also presented. |
| format | Article |
| id | doaj-art-7adfc7a126fb4770b7a17764a98334ec |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-7adfc7a126fb4770b7a17764a98334ec2025-02-03T01:03:09ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/38439213843921A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded VariationLaura Angeloni0Gianluca Vinti1Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, ItalyDipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, ItalyWe present a review on recent approximation results in the space of functions of bounded variation for some classes of integral operators in the multidimensional setting. In particular, we present estimates and convergence in variation results for both convolution and Mellin integral operators with respect to the Tonelli variation. Results with respect to a multidimensional concept of φ-variation in the sense of Tonelli are also presented.http://dx.doi.org/10.1155/2016/3843921 |
| spellingShingle | Laura Angeloni Gianluca Vinti A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation Journal of Function Spaces |
| title | A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation |
| title_full | A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation |
| title_fullStr | A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation |
| title_full_unstemmed | A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation |
| title_short | A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation |
| title_sort | review on approximation results for integral operators in the space of functions of bounded variation |
| url | http://dx.doi.org/10.1155/2016/3843921 |
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