?
Homeomorphic Changes of Variable and Fourier Multipliers
Cornell University
,
2019.
No. arXiv:1803.02177v2.
Lebedev V., Olevskii A.
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 h will sffice for all f in K. A similar result holds for functions on the torus T^d. This may be contrasted with the known solution of Luzin's problem related to the Wiener algebra.
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
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
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 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
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, / 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
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
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, / 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
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
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
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
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
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018
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
Amerik E., Verbitsky M., / Cornell University. Series arXiv "math". 2021.
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold ...
Added: April 7, 2022