Examinando por Autor "Barreto Melo, Samuel"
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Ítem Algunas propiedades de las matrices de Toeplitz complejasArdila Amado, Maicol Andres; Barreto Melo, SamuelThis monograph is using as a reference The chapter four of the article “On some properties of Toeplitz matrices ”, this article emphasizes Toeplitz matrices over the field of complex numbers. The objective of this monograph is to make an indepth study of the results given in the above mentioned article, for this I will show the step-by-step prove of each result, exemplifying the main results and giving some applications of these matrices. Mainly I made a study of the Frobenius and Operator norms defined over the subalgebra of Toeplitz matrices. One of the main results gives a relationship between the set M_n(C) and its respective subalgebra of Toeplitz matrices, this relationship can lead to the possible extension of the applications shown at the end of this monograph. Lin’s theorem has great importance since it is necessary to prove the aforementioned theorem. Another important result is the theorem 5.5 since it allows generalization to the area of C^{*} −algebras . Finally, one of the objectives in this monograph is to relate the circular matrices to the Discrete Fourier Transform (DFT), this relationship is given in chapter five with a study of the main properties of the DFT.Ítem Análisis de Fourier: de lo Clásico a lo AbstractoMolina Martínez, Julieth Katherine; Barreto Melo, SamuelThe pioneer article of Joseph Fourier allowed the advancement of mathematics in centuries 19th and 20th. Measure theory, topological groups theory and functional analysis were developed as answer to the questions proposed by Fourier. Problems were raised about the decomposition bt convolution of integrable functions on the real and complex field. Then, it was generalizing for locally compact abelian groups. In this discussion was included mathematicians as Rudin, Dieudonné, Zygmund, Salem, among others, getting famous factorization theorems. Cohen could carry these theorems to more abstracts environments as compact groups or Banach algebras. At the end of the 20th century, Saeki proved the Lp conjecture. We will rebuild the article "A trip from classical to abstract Fourier analysis" of Kenneth Ross published in 2014.Ítem Una aplicación de la fórmula de JensenPeña Moreno, Camila Andrea; Barreto Melo, SamuelThis work has the purpose to check the connection between the zero’s moduli of an analitic function on a disc with the function’s average , using the Jensen’s formula, seeing the multiple applications, the most important related with the growth of its zeros and the distribution. It’s important to look over some transcendentals theorems of complex variable, stablishing the behavior of the poles and zeros also its properties on a domain just as the relation between infinite products and sequence, this with the aim to demonstrate the formula in two different ways.Ítem Compresión de Imágenes con Wavelets y MiltiWavelets(Universidad Distrital Francisco José de Caldas) Barreto Melo, Samuel; Herrera García, Rodrigo JavierÍtem Construcción en expansión de Fourier de los polinomios de Apostol Frobenius- Euler y sus aplicacionesPlazas Buitrago, Julián Camilo; Barreto Melo, SamuelIn the present work, the Fourier expansion of the polynomials of Apostol Frobenius-Euler as will be seen in the main theorem. They make themselves known special cases of the Theorem; thus knowing the Fourier expansions of the Euler polynomials, Genocchi polynomials, Frobenius-Euler polynomials, the Apostol-Euler polynomials, the Apostol-Genocchi Polynomials. And I also know introduces the Apostol Frobenius-Genocchi polynomials. It will be seen that the polynomials of Apostol Frobenius-Genocchi are closely related to the polynomials by Apostol Frobenius-Euler.Ítem El dual en grupos Abelianos finitos - Teorema de PontryaginMartínez Salinas, Erika Johanna; Barreto Melo, SamuelIn the present graduate Monograph a first approximation is made to the duality theory about Finite abelian groups, distributed in 3 chapters: The first one contains the preliminaries about dual space from the algebraic point of view, that means in the vectors spaces and from the functional analysis point of view, in more general spaces like the normed spaces; definitions, theorems, corollaries and an entire collection of examples to understand the behaviour in dual space and subsequently to apply it into groups. In the second chapter is studied the convolution and the group algebra of a given group is created, also a very detailed description of its elements would be explained with examples and theorems which support the theory. In the third chapter we will introduce the duality in finite Abelian group’s topic, providing the group algebra presented in chapter two with a Hilbert´s space structure to subsequently talk about characters that will be of a great utility in the central theorem, Pontryagin's Duality Theorem for finite Abelian groups, at the end will be shown some examples which support the studied theory.Ítem Estabilidad en bases ortonormales y frames en espacios de HilbertPiñeros Parra, Carlos Mario; Barreto Melo, SamuelFrames have been studied as an algebraic concept which aims to generalize the orthonormal basis. Their unique properties allow to process information better and their coordinates hinder information being lost. Frames can serve as a tool for the processing of images and signals. These aforementioned characteristics were highlighted by studying frames on Hilbert Spaces. In order to study the concept in depth, frames were described under the conditions of finite dimensional spaces; by doing so, a connection between these and the Discrete Fourier Transform (DTF) was spotted. Then, this frames study was taken to infinite dimensional spaces finding a key relationship with the concept of Riesz basis. Finally, this work focuses on the stability in frames on Hilbert spaces.Ítem Estudio Comparativo entre los Frames y las Bases de RieszGómez Jiménez, Angela Nohelia; Barreto Melo, SamuelFrames are a convenient and flexible tool to obtain expansions in Hilbert spaces in a similar way as those via orthonormal bases. Therefore, we studied basic elements on the frames and bases of Riesz that allowed to compare them; seeing the relationship that exists with biortogonal systems, linear independence, w-independence, minimality and Schauder bases. And observing the features so that a frame does not contain a Schauder base and a Riesz frame contains a Riesz base .Ítem Funciones generalizadas y aplicacionesSantos Carrillo, David Felipe; Barreto Melo, Samuelit is talked by a lot of mathematicians how important is the theory of generalized functions in mathematics. The idea of this thesis is to do an introduction to this theory and show examples in Fourier's theory.Ítem Identification of multiple sclerosis brain lesions in magnetic resonance imaging using texture analysis(Universidad Distrital Francisco José de Caldas. Colombia) Aldana Ramírez, César Augusto; Orozco Higuera, Nelson Fabián; Barreto Melo, SamuelÍtem Introducción a las series de Fourier no armónicasMales Poveda, Daniel Camilo; Barreto Melo, SamuelIn the present document is desired to generalize the traditional Harmonic Fourier Series over a Hilbert space. First some concepts and results of functional analysis that will be useful are established. Then the concept of Frame is introduced, which is a tool in an advanced study of Non-Harmonic Fourier series. It follows with the study of the completeness of sequences in Hilbert spaces then in particular of the trigonometric system. Finally a reconstruction of the theory of Riesz Basis and Stability is done from the text “An Introduction to Non-Harmonic Fourier Series” of Robert M. Young, where Riesz basis are characterized and the Paley-Wiener theorem is introduced, which provides conditions so that the trigonometric system be stable in a Hilbert space under “sufficiently small” perturbations of integers.Ítem Una introducción a los wavelets complejos y filtrado de señalesGómez Fernández, Jhon Alejandro; Barreto Melo, SamuelIn this work, the main topics of the Fourier analysis will be addressed and later the Wavelet theme will be developed along with the multiresolution analysis to introduce the wavelet transform and the signal filtering following the text of "An Introduction to Wavelets Through Linear Algebra Undergraduate Texts in Mathematics "by Michael W. Frazier, along with the development of some examples.Ítem Medida de HaarLeandro Velosa, Camila Andrea; Barreto Melo, SamuelOne of the most useful properties of the measurement of Lebesgue integral is its invariance under translations and rotations. For example, if a ∈ R n, r ∈ R n × n and f is a Lebesgue integrable function on R n, then Z Rn f (x) dx = Z Rn f (rx + a) dx. The notion of Haar measure is a generalization of this example. In this sense in a (more generally locally compact) compact group G, there is a measure m such that ZG f (x) dm (x) = ZG f (bx) dm (x), for an integrable function f on G and element b ∈ G. This measure was introduced by Alfred Haar, Hungarian mathematician, in 1933. "The proof that there is an invariant measure on a locally compact and 'separable group. Later Banach theorem generalizes axiomatically defining congruence. In addition severability it is not essential in the work of Banach, as their arguments are valid by replacing sequential compactness compactness. Finally Haar's theorem was generalized to locally compact groups and completed in 1936 with the uniqueness theorem Von Neumann because "Ítem Método de Wavelet-Galerkin para Ecuaciones DiferencialesSánchez Navarro, Juan Manuel; Barreto Melo, SamuelThis work will explain first the Galerkin's method for solve differential equations, second the definition of Wavelet and construction of it, third the reconstruction of method of wavelet-Galerkin meanly developed in the sixth chapter of “An Introduction to Wavelets Through Linear Algebra Undergraduate Texts in Mathematics” by Michael W. Frazier for solve Sturm-Liouville's equations as well as a detailed explanation of some examples and comparisons with other methods introduced by the article "Wavelet-galerkin solution of some ordinary differential equations" by Hadzi Katerina and Jasmina Buralieva.Ítem Teorema de Plancherel para Grupos Abelianos Localmente CompactosGonzález Ramos, Laura Melissa; Barreto Melo, SamuelIn this paper we will study the Fourier transform of defined functions on locally compact groups to then present the Plancherel theorem and some of its applicationsÍtem El Teorema de representación de riesz en espacios de Hausdorff localmente compactosPuentes Saénz, Edith Sofía; Barreto Melo, SamuelIn the harmonic analysis in locally compact abelian groups reference is made to a special integral. What is the measure that gives rise to this integral? The answer is given by Riesz's Representation Theorem. This theorem, along with its different versions, describes the conjugate space of the topological vector spaces establishing a connection between the linear functionalities and the measures.Ítem La transformada de Fourier fraccional y algunas aplicacionesHerrera Montoya, Miguel Alberto; Ramírez Beltrán, Carlos Andrés; Barreto Melo, SamuelFirst, fractional calculation is introduced with the aim of presenting the derived and integral operators and talking about their fractional powers. Second, the kernel deduction of the fractional Fourier transform (FRFT) is made using the known time-frequency representations and facts of the classical Fourier transform, then alternative definitions, some equivalents, are given. Third, some of these definitions are implemented by applying them to one-dimensional signals using a mathematical sotware, Matlab. Fourth, the Fractional Fourier transform is implemented in some fields of application.