Some historical-analytical aspects of functional analysis
DOI:
https://doi.org/10.17268/sel.mat.2021.02.15Keywords:
Calculus of variations, Dirichlet principle, operators, Hilbert spaces, distributionsAbstract
In ten sections we present an overview of the evolution of functional analysis, from the calculus of variations to partial differential operators, through integral equations and the contributions made in the first half of the 20th century.
References
Banach S. Théorie des Opérations Linéaires. Warszawa. 1932.
Bombal F. Los Orígenes del Análisis Funcional. Real Acad. de Ciencias de Madrid. 1994.
Dieudonné J. History of Functional Analysis. North-Holland Elsevier Sc. 1983.
Figueiredo D. Teoría Classica do Potencial. U. N. Brasilia. 1963.
Figueiredo D. Introducao as Equacoes Integrais. Escola de Análise. Sao Paulo. 1977.
Gelfand IM. Análisis Funcional. Dentro de la Matemática: su contenido, métodos y significado. Alianza Editorial. Vol. 3. Madrid. 1973.
Kline M. El Pensamiento Matemático de la Antigüedad a nuestros Días. Alianza Editorial. Madrid. 2012.
Ortíz A. Tópicos sobre Ecuaciones en Derivadas Parciales. Internet. PUCP. 2004.
Ortíz A. La Matemática a Través de Clásicas Áreas. Vol. 3. Internet. PUCP. 2017.
Ortíz A. Some Ideas on the Genesis of the Infinitesimal Calculus. Selecciones Matemáticas. 2021; 8(1):173–195.
Ortíz, A. Some Ideas on the Evolution of Real Mathematical Analysis. Selecciones Matemáticas. 2021; 8(1):196–217.
Pietsch A. History of Banach Spaces and Linear Operators. Birkhäser. Boston. 2007.
Riesz F, Nagy B. Functional Analysis. Frederick Ungar. Pub. 1955.
Stone M. Linear Transformations in Hilbert Space and their Applications to Analysis. Am. Math. Soc. N. York. 1932.
Treves F, Figueiredo D. Espacos Vetoriais Topológicos e Distribuicoes. Notas de Mat. 41IMPA. Brasil. 1968.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Selecciones Matemáticas
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.
