Nonlinear Integral Operators and Applications
Language: English
Published by De Gruyter, 2003
Series: Book 3 of 39 - De Gruyter Series in Nonlinear Analysis and Applications
- Hardcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
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Condition: New
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Druck auf Anfrage Neuware - Printed after ordering - 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.…
Seller Inventory # 9783110175516
- Title
- Nonlinear Integral Operators and Applications
- Author
- Gianluca Vinti
- Publisher
- De Gruyter
- Publication year
- 2003
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 3110175517
- ISBN 13
- 9783110175516
- Item weight
- 553 grams
- Dimensions
- 246x175x17 mm
- Series
- Book 3 of 39: De Gruyter Series in Nonlinear Analysis and Applications
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.
"Synopsis" may belong to another edition of this title.
About the Author
Carlo Bardaro and Gianlica Vinti are Professors at the Mathematics Departments of the University of Perugia, Italy.
Julian Musielak is Professor at the Faculty of Mathematics and Computer Science of the University of Poznan, Poland.
"About the title" may belong to another edition of this title.
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