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О топологической устойчивости непрерывных функций в некоторых пространствах, связанных с рядами Фурье
Известия РАН. Серия математическая. 2010. Т. 74. № 2. С. 131-164.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
Vladimir Lebedev, / Cornell University. Series math "arxiv.org". 2015. No. 1508.06673.
We consider the class C(T) of continuous real-valued functions on the circle. For certain classes of functions naturally characterised by the rapidity of decrease of Fourier coefficients we investigate whether it is possible to bring families of functions in C(T) into these classes by a change of variable. This paper was originally published in Matematicheskii ...
Added: September 8, 2015
V. V. Lededev, Izvestiya. Mathematics 2010 Vol. 74 No. 2 P. 347-378
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators in these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case. ...
Added: April 12, 2012
V. V. Lebedev, Functional Analysis and Its Applications 2017 Vol. 51 No. 2 P. 148-151
It is well--known that certain
properties of continuous functions on the circle T,
related to the Fourier expansion, can be improved by a change
of variable, i.e., by a homeomorphism of the circle onto
itself. One of the results in this area is the Jurkat--Waterman
theorem on conjugate functions, which improves the classical
Bohr--P\'al theorem. In the present work we propose ...
Added: June 29, 2017
Vladimir Lebedev, / Cornell University. Series math "arxiv.org". 2015. No. 1508.07167.
The well-known Bohr--Pal theorem asserts that for every continuous real-valued function f on the circle T there exists a change of variable, i.e., a homeomorphism h of T onto itself, such that the Fourier series of the superposition f o h converges uniformly. Subsequent improvements of this result imply that actually there exists a homeomorphism ...
Added: September 3, 2015
Vladimir Lebedev, Studia Mathematica 2015 Vol. 231 No. 1 P. 73-81
The well-known Bohr--Pal theorem
asserts that for every continuous real-valued function f on
the circle T there exists a change of variable, i.e.,
a homeomorphism h of T onto itself, such that the
Fourier series of the superposition foh converges
uniformly. Subsequent improvements of this result imply that
actually there exists a homeomorphism that brings f into the
Sobolev space W_2^{1/2}(T). This ...
Added: February 16, 2016
В. В. Лебедев, Функциональный анализ и его приложения 2017 Т. 51 № 2 С. 87-91
It is well--known that certain
properties of continuous functions on the circle T,
related to the Fourier expansion, can be improved by a change
of variable, i.e., by a homeomorphism of the circle onto
itself. One of the results in this area is the Jurkat--Waterman
theorem on conjugate functions, which improves the classical
Bohr--Pal theorem. In the present work we propose ...
Added: June 29, 2017
Belousov F., Бекларян Л. А., Дифференциальные уравнения 2015 Т. 51 № 12 С. 1565-1579
Работа посвящена периодическим решениям функционально-дифференциального уравнения точечного типа. В терминах правой части исходного нелинейного функционально-дифференциального уравнения точечного типа будут сформулированы легко проверяемые условия существования и единственности w-периодического решения, описан итерационный процесс построения такого решения, а также указана скорость сходимости итерационного процесса. ...
Added: April 9, 2015
Goncharuk N. B., Функциональный анализ и его приложения 2012 Т. 46 № 1 С. 13-30
По заданному диффеоморфизму окружности f можно построить отображение, переводящее вещественное число a в число вращения диффеоморфизма f+a. В 1978 г. В. И. Арнольд предложил комплексный аналог этого отображения: каждое число z, Imz>0, переходит в модуль μ(z) эллиптической кривой, которая строится по отображению f+z. В предлагаемой статье исследовано поведение отображения μ вблизи отрезков вещественной оси, на ...
Added: February 18, 2013
V. V. Lebedev, Mathematical notes 2011 Vol. 90 No. 3 P. 373-384
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: ...
Added: April 12, 2012
Голубева З. Н., Ерастова Н. К., М. : МИЭМ НИУ ВШЭ, 2013
Приводятся теоретические понятия и типовые задачи с решениями для выполнения домашних и аудиторных контрольных работ 3, 4 модулей по математическому анализу для студентов инженерных факультетов. ...
Added: March 14, 2013
V. V. Lebedev, Sbornik Mathematics 2010 Vol. 201 No. 12 P. 1811-1836
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase. ...
Added: April 12, 2012
Polyakov I. V., Математические заметки 2015
В данной работе рассмотрены максимальные операторы средних Марцинкевича рядов Фурье по переставленной системе Уолша-Пэли. Исследованы типы и слабые типы данных операторов для различных классов перестановок системы Уолша-Пэли. ...
Added: October 25, 2014
В. В. Лебедев, Математические заметки 2011 Т. 90 № 3 С. 394-407
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: ...
Added: April 12, 2012
V. V. Lebedev, / Cornell University. Series math "arxiv.org". 2016. No. 1603.04539.
It is well--known that certain
properties of continuous functions on the circle $\mathbb T$,
related to the Fourier expansion, can be improved by a change
of variable, i.e., by a homeomorphism of the circle onto
itself. One of the results in this area is the Jurkat--Waterman
theorem on conjugate functions, which improves the classical
Bohr--Pal theorem. In the present work we ...
Added: November 10, 2016
В. В. Лебедев, Математический сборник 2010 Т. 201 № 12 С. 103-130
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase. ...
Added: April 12, 2012
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20
We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...
Added: March 13, 2016