Nonlinear Integral Operators and Applications / / Carlo Bardaro, Julian Musielak, Gianluca Vinti.
In 1903 Fredholm published his famous paper on integral equations. Since then linear integral operators have become an important tool in many areas, including the theory of Fourier series and Fourier integrals, approximation theory and summability theory, and the theory of integral and differential...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2008] ©2003 |
Year of Publication: | 2008 |
Language: | English |
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Bardaro, Carlo, author. aut http://id.loc.gov/vocabulary/relators/aut Nonlinear Integral Operators and Applications / Carlo Bardaro, Julian Musielak, Gianluca Vinti. Berlin ; Boston : De Gruyter, [2008] ©2003 1 online resource (201 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Series in Nonlinear Analysis and Applications , 0941-813X ; 9 Frontmatter -- Contents -- Chapter 1. Kernel functionals and modular -- spaces -- Chapter 2. Absolutely continuous modulars and -- moduli of continuity -- Chapter 3. Approximation by convolution type -- operators -- Chapter 4. Urysohn integral operators with -- homogeneous kernel functions. Applications to nonlinear Mellin-type -- convolution operators -- Chapter 5. Summability methods by convolution-type -- operators -- Chapter 6. Nonlinear integral operators in the -- space BVϕ -- Chapter 7. Application to nonlinear integral -- equations -- Chapter 8. Uniform approximation by sampling type -- operators. Applications in signal analysis -- Chapter 9. Modular approximation by sampling type -- operators -- Backmatter restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star In 1903 Fredholm published his famous paper on integral equations. Since then linear integral operators have become an important tool in many areas, including the theory of Fourier series and Fourier integrals, approximation theory and summability theory, and the theory of integral and differential equations. As regards the latter, applications were soon extended beyond linear operators. In approximation theory, however, applications were limited to linear operators mainly by the fact that the notion of singularity of an integral operator was closely connected with its linearity. This book represents the first attempt at a comprehensive treatment of approximation theory by means of nonlinear integral operators in function spaces. In particular, the fundamental notions of approximate identity for kernels of nonlinear operators and a general concept of modulus of continuity are developed in order to obtain consistent approximation results. Applications to nonlinear summability, nonlinear integral equations and nonlinear sampling theory are given. In particular, the study of nonlinear sampling operators is important since the results permit the reconstruction of several classes of signals. In a wider context, the material of this book represents a starting point for new areas of research in nonlinear analysis. For this reason the text is written in a style accessible not only to researchers but to advanced students as well. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Integral operators. Nonlinear operators. Integraloperator. Nichtlinearer Operator . MATHEMATICS / General. bisacsh Musielak, Julian, author. aut http://id.loc.gov/vocabulary/relators/aut Vinti, Gianluca, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications 9783110647099 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2008 9783110212129 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008 9783110212136 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008 9783110209082 ZDB-23-DMN print 9783110175516 https://doi.org/10.1515/9783110199277 https://www.degruyter.com/isbn/9783110199277 Cover https://www.degruyter.com/document/cover/isbn/9783110199277/original |
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Bardaro, Carlo, Bardaro, Carlo, Musielak, Julian, Vinti, Gianluca, |
spellingShingle |
Bardaro, Carlo, Bardaro, Carlo, Musielak, Julian, Vinti, Gianluca, Nonlinear Integral Operators and Applications / De Gruyter Series in Nonlinear Analysis and Applications , Frontmatter -- Contents -- Chapter 1. Kernel functionals and modular -- spaces -- Chapter 2. Absolutely continuous modulars and -- moduli of continuity -- Chapter 3. Approximation by convolution type -- operators -- Chapter 4. Urysohn integral operators with -- homogeneous kernel functions. Applications to nonlinear Mellin-type -- convolution operators -- Chapter 5. Summability methods by convolution-type -- Chapter 6. Nonlinear integral operators in the -- space BVϕ -- Chapter 7. Application to nonlinear integral -- equations -- Chapter 8. Uniform approximation by sampling type -- operators. Applications in signal analysis -- Chapter 9. Modular approximation by sampling type -- Backmatter |
author_facet |
Bardaro, Carlo, Bardaro, Carlo, Musielak, Julian, Vinti, Gianluca, Musielak, Julian, Musielak, Julian, Vinti, Gianluca, Vinti, Gianluca, |
author_variant |
c b cb c b cb j m jm g v gv |
author_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
Musielak, Julian, Musielak, Julian, Vinti, Gianluca, Vinti, Gianluca, |
author2_variant |
j m jm g v gv |
author2_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author_sort |
Bardaro, Carlo, |
title |
Nonlinear Integral Operators and Applications / |
title_full |
Nonlinear Integral Operators and Applications / Carlo Bardaro, Julian Musielak, Gianluca Vinti. |
title_fullStr |
Nonlinear Integral Operators and Applications / Carlo Bardaro, Julian Musielak, Gianluca Vinti. |
title_full_unstemmed |
Nonlinear Integral Operators and Applications / Carlo Bardaro, Julian Musielak, Gianluca Vinti. |
title_auth |
Nonlinear Integral Operators and Applications / |
title_alt |
Frontmatter -- Contents -- Chapter 1. Kernel functionals and modular -- spaces -- Chapter 2. Absolutely continuous modulars and -- moduli of continuity -- Chapter 3. Approximation by convolution type -- operators -- Chapter 4. Urysohn integral operators with -- homogeneous kernel functions. Applications to nonlinear Mellin-type -- convolution operators -- Chapter 5. Summability methods by convolution-type -- Chapter 6. Nonlinear integral operators in the -- space BVϕ -- Chapter 7. Application to nonlinear integral -- equations -- Chapter 8. Uniform approximation by sampling type -- operators. Applications in signal analysis -- Chapter 9. Modular approximation by sampling type -- Backmatter |
title_new |
Nonlinear Integral Operators and Applications / |
title_sort |
nonlinear integral operators and applications / |
series |
De Gruyter Series in Nonlinear Analysis and Applications , |
series2 |
De Gruyter Series in Nonlinear Analysis and Applications , |
publisher |
De Gruyter, |
publishDate |
2008 |
physical |
1 online resource (201 p.) Issued also in print. |
contents |
Frontmatter -- Contents -- Chapter 1. Kernel functionals and modular -- spaces -- Chapter 2. Absolutely continuous modulars and -- moduli of continuity -- Chapter 3. Approximation by convolution type -- operators -- Chapter 4. Urysohn integral operators with -- homogeneous kernel functions. Applications to nonlinear Mellin-type -- convolution operators -- Chapter 5. Summability methods by convolution-type -- Chapter 6. Nonlinear integral operators in the -- space BVϕ -- Chapter 7. Application to nonlinear integral -- equations -- Chapter 8. Uniform approximation by sampling type -- operators. Applications in signal analysis -- Chapter 9. Modular approximation by sampling type -- Backmatter |
isbn |
9783110199277 9783110647099 9783110637205 9783110212129 9783110212136 9783110209082 9783110175516 |
issn |
0941-813X ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA329 |
callnumber-sort |
QA 3329.6 |
url |
https://doi.org/10.1515/9783110199277 https://www.degruyter.com/isbn/9783110199277 https://www.degruyter.com/document/cover/isbn/9783110199277/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515/.723 |
dewey-sort |
3515 3723 |
dewey-raw |
515/.723 |
dewey-search |
515/.723 |
doi_str_mv |
10.1515/9783110199277 |
oclc_num |
979837968 |
work_keys_str_mv |
AT bardarocarlo nonlinearintegraloperatorsandapplications AT musielakjulian nonlinearintegraloperatorsandapplications AT vintigianluca nonlinearintegraloperatorsandapplications |
status_str |
n |
ids_txt_mv |
(DE-B1597)32447 (OCoLC)979837968 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2008 Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008 |
is_hierarchy_title |
Nonlinear Integral Operators and Applications / |
container_title |
Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications |
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