Academic Journal
Approximation of Almost Diagonal Non-linear Maps by Lattice Lipschitz Operators
| العنوان: | Approximation of Almost Diagonal Non-linear Maps by Lattice Lipschitz Operators |
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| المؤلفون: | Arnau-Notari, Andres Roger, Calabuig, J. M., Erdogan, Ezgi, Sánchez Pérez, Enrique Alfonso |
| المساهمون: | Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos - Escola Tècnica Superior d'Enginyers de Camins, Canals i Ports, Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros Industriales - Escola Tècnica Superior d'Enginyers Industrials, Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada, Agencia Estatal de Investigación, Universitat Politècnica de València |
| بيانات النشر: | Springer-Verlag |
| سنة النشر: | 2024 |
| المجموعة: | Universitat Politécnica de Valencia: RiuNet / Politechnical University of Valencia |
| مصطلحات موضوعية: | Lattice, Non-linear map, Lipschitz operator, Normed space, Diagonalisation, MATEMATICA APLICADA |
| الوصف: | [EN] Lattice Lipschitz operators define a new class of nonlinear Banach-lattice-valued maps that can be written as diagonal functions with respect to a certain basis. In the n-dimensional case, such a map can be represented as a vector of size n of real-valued functions of one variable. In this paper we develop a method to approximate almost diagonal maps by means of lattice Lipschitz operators. The proposed technique is based on the approximation properties and error bounds obtained for these operators, together with a pointwise version of the interpolation of McShane and Whitney extension maps that can be applied to almost diagonal functions. In order to get the desired approximation, it is necessary to previously obtain an approximation to the set of eigenvectors of the original function. We focus on the explicit computation of error formulas and on illustrative examples to present our construction. ; The first author was supported by a contract of the Programa de Ayudas de Investigacion y Desarrollo (PAID-01-21), Universitat Politecnica de Valencia. This publication is part of the R & D & I project PID2020-112759GB-I00 funded by MCIN/AEI /10.13039/501100011033. This publication is part of the R & D & I project PID2022-138342NB-I00 funded by MCIN/AEI /10.13039/501100011033. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. ; Arnau-Notari, AR.; Calabuig, JM.; Erdogan, E.; Sánchez Pérez, EA. (2024). Approximation of Almost Diagonal Non-linear Maps by Lattice Lipschitz Operators. Bulletin of the Brazilian Mathematical Society New Series. 55(1). https://doi.org/10.1007/s00574-024-00385-9 ; 55 ; 1 |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| تدمد: | 1678-7544 |
| Relation: | Bulletin of the Brazilian Mathematical Society New Series; info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-112759GB-I00/ES/METAESTRUCTURAS HIPERUNIFORMES/; info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-138342NB-I00/ES/TECNICAS DE ANALISIS FUNCIONAL EN PROBLEMAS DE APROXIMACION Y APLICACIONES/; info:eu-repo/grantAgreement/UPV//PAID-01-21/; https://doi.org/10.1007/s00574-024-00385-9; urn:issn:1678-7544; http://hdl.handle.net/10251/203933 |
| DOI: | 10.1007/s00574-024-00385-9 |
| الاتاحة: | http://hdl.handle.net/10251/203933 https://doi.org/10.1007/s00574-024-00385-9 |
| Rights: | http://creativecommons.org/licenses/by/4.0/ ; info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsbas.8BBF0C38 |
| قاعدة البيانات: | BASE |
| تدمد: | 16787544 |
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| DOI: | 10.1007/s00574-024-00385-9 |