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Количественные оценки в теоремах типа теоремы Берлинга-Хелсона
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.
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
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
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
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
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
Lebedev V., Olevskii A., / Cornell University. Series math "arxiv.org". 2019. No. arXiv:1803.02177v2.
We consider the algebras M_p of Fourier multipliers and show that for every bounded continuous function f on R^d there exists a self-homeomorphism h of R^d such that the superposition f oh is in M_p(R^d) for all p, 1 < p < \infty. Moreover, under certain assumptions on a family K of continuous functions, one ...
Added: May 8, 2018
Vladimir Lebedev, Studia Mathematica 2019 Vol. 247 No. 3 P. 273-283
We consider the Wiener algebra A(T^d) of absolutely convergent Fourier series on the d-torus. For phase functions \phi of a certain special form we obtain lower bounds for the A -norms of e^{i\lambda\varphi} as \lambda tends to \infty. ...
Added: March 23, 2018
Chistyakov V., Solycheva O. M., Journal of difference equations and applications 2003 Vol. 9 No. 3-4 P. 407-416
We present necessary and sufficient conditions on the generating functions of operators of substitution (Nemytskii superposition operators), which map the Waterman space λBV of functions of λ-bounded variation on the interval into another space of this type and satisfy the Lipschitz condition. ...
Added: December 4, 2012
Lebedev V., Olevskii A., Journal of Mathematical Analysis and Applications 2020 Vol. 481 No. 2 Article 123502
We consider the algebras M_p of
Fourier multipliers and show that for every bounded continuous
function f on R^d there exists a self-homeomorphism
h of R^d such that the superposition foh$ is
in M_p(R^d) for all p, 1<p<\infty. Moreover,
under certain assumptions on a family K of continuous
functions, one h will suffice for all f\in K. A similar
result holds for ...
Added: October 16, 2019
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
Vladimir Lebedev, / Cornell University. Series math "arxiv.org". 2017. No. arXiv:1611.01739v4.
We concider the Wiener algebra A(T^d) of absolutely convergent Fourier series on the d -torus. For phase functions \phi of a certain special form we obtain lower bounds for the A -norms of e^{i\lambda\phi} as \lambda tends to \infty. ...
Added: November 11, 2016
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
В. В. Лебедев, Математический сборник 2012 Т. 203 № 11 С. 121-128
We consider the Paley--Wiener spaces of L2 -functions whose Fourier transform has a bounded support. We show that every continuous mapping that generates a superposition operator acting on these spaces is affine and injective. ...
Added: February 13, 2013
V. V. Lebedev, Sbornik Mathematics 2012 Vol. 203 No. 11 P. 1647-1653
We consider the Paley--Wiener spaces of L2-functions whose Fourier transform has a bounded support. We show that every continuous mapping that generates a superposition operator acting on these spaces is affine and injective. ...
Added: January 29, 2013
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
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
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
В. В. Лебедев, 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. ...
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
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
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