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Item type:Publication, Some historical-analytical aspects of functional analysis(Universidad Nacional de Trujillo, 2021-11-30)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. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Singular integral operators, a brief historical overview of its evolution(Universidad Nacional de Trujillo, 2022-06-30)In this work we give an analytical-historical view of the classical theory of singular integrals introduced by A.P. Calderón-A. Zygmund. Emphasis is given to their applications to PDEs and to some projections of the theory. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, ¿Qué tan grande es el infinito? ¡El infinito … ya no nos asusta!(2024-07-26)El objetivo de este artículo es presentar en forma breve y no – técnica la idea del infinito, desde la época de los antiguos griegos hasta los siglos XIX Y XX, dando énfasis a George Cantor y su teoría de conjuntos.1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Harmonic analysis and partial differential equations: Brief walk through these domains(Universidad Nacional de Trujillo, 2024-11-30)In this walk we are going to walk through some domains of harmonic analysis and partial differential equations (PDE). The objective of this article is to motivate students and colleagues to study these beautiful areas of analysis and therefore we emphasize the ideas, some mathematical results and some historical data. In this “ tourist” tour we will see a panorama of such areas in the 19th and 20 th centuries, a panorama of the Fourier series; we give a vision of the theory of distributions, of the theory of linear partial differential operators and we culminate by given a vision of harmonic analysis and its relationship we the PDE. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Brief to distributions and to Hörmander spaces Bp,k(Universidad Nacional de Trujillo, 2024-11-30)Partial differential equations (PDE’s) are, we believe, little known in our country, especially at a medium-advanced level, in particular, their historical roots and methods developed in their evolution. The objective of this article is to contribute to a knowledge in this direction especially to colleagues and students who are interested in studying and researching in this central Branch of mathematics. As a model we have chosen H¨ormander’s book, [1], whose study and teaching will be a sign of great progress in this direction in our country. In this article we only give an to part I dedicated to functional analysis and which includes chapters I and II that deal with the theory of distributions and some special spaces of distributions, respectively. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Some aspects in the PDE: The Dirichlet and the Cauchy problems(Universidad Nacional de Trujillo, 2024-06-30)In this article we present two classic problems in PDE: the Dirichlet problem and the Cauchy problem. Some ideas are previously discussed, such as functions and identities’s Green, and “bad positions” problems. The work of L. Nirenberg [1] is discussed in detail where some results of L.Hörmander [2] are used. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, The integral, a vision of its evolution through time IV: Harmonic analysis, stochastic processes, stochastic integration(Universidad Nacional de Trujillo, 2024-06-30)The objective of this article is to give an overview of the relationship between harmonic analysis and stochastic processes, a relationship that has motivated many investigations and applications to specific problems. We will also emphasize stochastic integration. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, The Integral, a Vision of Its Evolution Through Time II(Universidad Nacional de Trujillo, 2023-11-30)In this part II we intend to give an overview of the different ways in which the idea of integral has evolved over time; in particular the Riemann integral has been the motivation for further research up to the present. We only want to motivate this part of the history of mathematical analysis in our environment with the aim that student and teachers have a guide for more detailed studies and thus contribute to the development of matematics in our region. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, The Integral, a Vision of Its Evolution Through Time III(Universidad Nacional de Trujillo, 2023-11-30)In this opportunity we present some areas of the evolution of the integral, which complement what was deal with in parts I and II. Thus we give a conceptual overview of the McShane integral, of the C-integral, of the Bochner integral, of the Lm HK integral , of the integral on manifolds and on a modern point of view of the Riemann integral. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, La integral: una visión de su evolución a través del tiempo I(Universidad Nacional de Trujillo, 2023-07-26)This article is the first part of one that has three parts. In the first one we present a vision of the evolution of the idea of integral, from ancient Greece to the Lebesgue integral. In the second part we will present how the Riemann integral has been investigated towards a unified theory of the integral.