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Поведение тригонометрических рядов Фурье в классах φ(L), близких к L : магистерская диссертация / Behavior of trigonometric Fourier series in classes φ(L) close to LГабдуллин, М. Р., Gabdullin, M. R. January 2015 (has links)
We study the behavior of trigonometric Fourier series in classes φ(L) close to L. We prove that recent Fillipov's result on the convergence of trigonometric Fourier series in classes φ(L) containing L cannot be improved. In the case when the function φ(u) defining the class φ(L) grows at infinity slower than up for all p>1, we that a famous result on the convergence of trigonometric Fourier series in the classes φ(L) containing in L cannot be improved. / Изучается поведение тригонометрических рядов Фурье в пространствах φ(L), близких к L. Доказана неулучшаемость недавнего результата В.И.Филиппова о сходимости тригонометрического ряда Фурье в пространствах φ(L), содержащих в L. В случае, когда функция φ(u), задающая класс φ(L), на бесконечности растёт медленнее, чем up при всех p>1, показана неулучшаемость известного результата о сходимости тригонометрического ряда Фурье в пространстве φ(L), содержащемся в L.
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Неравенство Бернштейна для тригонометрических полиномов для пары пространств L0 и L2 : магистерская диссертация / Bernstein inequality for trigonometric polynomials for the pair of spaces L0 and L2Микора, М. Н., Mikora, M. N. January 2015 (has links)
We study the best constant C(n) in the Bernstein inequality between the L0-norm of the first derivative of a trigonometric polynomial and the L2-norm of the polynomial itself on the set of trigonometric polynomials of a given degree n ≥1 with real coefficients. We prove that on the subset of polynomials from Tn such that all zeros of the derivative of a polynomial are real, the Bernstein inequality holds with the constant n/√2. In the general case, we obtain the close two-sided estimates: n/√2≤C(n)≤n. / Изучается наилучшая константа C(n) в неравенстве Бернштейна между L0-нормой первой производной тригонометрического полинома и L2-нормой самого полинома на
множестве Tn тригонометрических полиномов заданного порядка n ≥1 с вещественными коэффициентами. Показано, что на подмножестве полиномов из Tn, все нули производной которых вещественные, неравенство Бернштейна имеет место с константой n/√2. В общем случае для константы C(n) получены близкие двусторонние оценки n/√2≤C(n)≤n.
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О неравенстве Тайкова для сопряженных тригонометрических полиномов : магистерская диссертация / On the Taikov inequality for conjugate trigonometric polynomialsСерков, А. О., Serkov, A. O. January 2015 (has links)
We study a Szego type inequality between the uniform norm of a fractional derivative of a conjugate trigonometric polynomial and the uniform norm of the polynomial itself. We prove that a set of extremal polynomials in the Szego inequality for the zero-order derivative on the set of trigonometric polynomials, in addition to odd polynomials found earlier by L.V.Taikov, contains even polynomials. We also describe the whole class of extremal polynomials / Изучается неравенство типа Сеге между равномерной нормой производной дробного порядка сопряженного тригонометрического полинома и равномерной нормой самого полинома.
Доказано, что в неравенстве Сеге для производной нулевого порядка на множестве тригонометрических полиномов имеются как нечетные, найденные ранее Л.В.Тайковым, так и четные экстремальные полиномы. Также полностью описан класс экстремальных полиномов для данного случая.
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Тригонометрические и алгебраические полиномы с несколькими фиксированными старшими гармониками, наименее уклоняющиеся от нуля : магистерская диссертация / Trigonometric and algebraic polynomials with several fixed higher harmonics that deviate least from zeroРожин, А. А., Rozhin, A. A. January 2017 (has links)
Рассматривается задача о полиномах с фиксированными коэффициентами при старших гармониках, наименее уклоняющихся от нуля. В явном виде выписаны все тригонометрические полиномы с фиксированными коэффициентами при трех старших гармониках, наименее уклоняющиеся от нуля в интегральной норме, а также алгебраические многочлены с тремя фиксированными старшими коэффициентами, наименее уклоняющиеся от нуля в интегральной норме с весом Чебышева. / We consider the problem on polynomials with fixed higher coefficients that deviate least from zero. We find an explicit form for all trigonometric polynomials with fixed coefficients at three highest harmonics that deviate least from zero in the integral norm as well as algebraic polynomials with three fixed leading coefficients that deviate least from zero in the integral norm with the Chebyshev weight.
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Solution de C. Hyltén-Cavallius pour un problème de P. Turán concernant des polynômesTinawi, Félix January 2008 (has links)
Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.
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Números complexos para professores de matemática da educação básica que atuam no ensino médio / Complex number for high school mathematics teachersCruz Filho, Robinson Antão da 13 April 2018 (has links)
Um texto sobre o corpo dos números complexos abordando-os de uma forma integrada e direcionada para professores de educação básica que atuam no ensino médio. Apresenta de forma bem fundamentada vários aspectos dos números complexos: par ordenado, vetor do plano, forma algébrica, forma trigonométrica e matricial. Todos os resultados essenciais foram demonstrados. Há um capítulo com alguns problemas resolvidos. / A text on the field of complex numbers in an integrated way and directed to teachers of basic education who work in high school. It presents in a well-founded form several aspects of the complex numbers: ordered pair, plane vector, algebraic form, trigonometric and matrix form. For every essential result, there is a proof. There is a chapter with some solved problems.
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"Funções e polinômios univalentes: algumas propriedades e aplicações" / Univalent functions and polynomials: some properties and applicationsBertoni, Vanessa 31 July 2006 (has links)
O objetivo principal deste trabalho é o estudo das funções univalentes e de suas propriedades. Este estudo é direcionado principalmente aos polinômios univalentes e à investigação de prolemas extremos envolvendo seus coeficientes, seus zeros e suas propriedades geométricas. Encontramos uma relação interessante entre os polinômios univalentes e os polinômios univalentes definida por Suffridge. Geramos várias funções univalentes estreladas e convexas através de suas propriedades geométricas e da localização de seus zeros. / The main aim of this work is the study of univalent functions and their properties. This study is focused speciall on the univalent polynomials and theinvestigation of extremal problems involving their coefficients, zeros and geometric properties. We find a very ineresting relation between univalent polynomials through a class of univalent starlike and convex functions involving their geometric properties and the location of their zeros.
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A função periódica para o ensino médioAbrantes, Wagner Gomes Barroso 12 January 2015 (has links)
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Previous issue date: 2015-01-12 / Não Informada / The periodic functions are a topic of enormous importance for the High School. This Labor
Completion of course covers the basics for understanding the topic, the characteristics of
these functions and those with whom students have contact in basic education. The use
of computational resources in the teaching of Periodic Functions and their applications
are also part of the research. / As funções periódicas constituem um tema de enorme relevância para o Ensino Médio.
Este Trabalho de Conclusão de Curso aborda os conceitos básicos para a compreensão do
tema, as características dessas funções e aquelas com as quais os alunos tem contato
na educação básica. O emprego dos recursos computacionais no ensino das Funções
Periódicas e suas aplicações também fazem parte da pesquisa.
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Solution de C. Hyltén-Cavallius pour un problème de P. Turán concernant des polynômesTinawi, Félix January 2008 (has links)
Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal
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Polinômios de Szegö e análise de frequênciaMilani, Fernando Feltrin [UNESP] 21 July 2005 (has links) (PDF)
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milani_ff_me_sjrp.pdf: 539043 bytes, checksum: b4613024414cd9fa758d64376a046176 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / O objetivo deste trabalho é estudar os polinômios de Szegõ, que são ortogonais no círculo unitário, e suas relações com certas frações contínuas de Perron-Carathéodory e quadratura no círculo unitário, afim de resolver o problema de momento trigonométrico. Além disso, estudar a utilização dos polinômios de Szegõ na determinação das freqüências de um sinal trigonométrico em tempo discreto xN(m). Para isso, investigamos os polinômios de Szegõ gerados por uma medida N definida através do sinal trigonométrico xN(m), para m = 0, 1, 2,...N -1, e o comportamento dos zeros desses polinômios quando N_8. / The purpose here is to study the orthogonal polynomials on the unit circle, known as Szegõ polynomials, and the relations to Perron- Carathéodory continued fractions, and quadratures on the unit circle in order to solve the trigonometric moment problem. Another purpose is to study how the Szegõ polynomials can be used to determine the frequencies from a discrete time trigonometric signal xN(m). We investigate the Szegõ polynomials associated with a measure N defined by the trigonometric sinal xN(m), m = 0, 1, 2, ...N -1. We study the behaviour of zeros of these polynomials when N 8.
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