Приближения полиномами от двоякопериодических функций Вейерштрасса

?

Приближения полиномами от двоякопериодических функций Вейерштрасса

Вестник Санкт-Петербургского университета. Серия 1. Математика. Механика. Астрономия. 2023. Т. 10. № 1. С. 61–72.

Shirokov N. A., Синцова К. А.

The problem of describing classes of functions in terms of the rate of approximation of these functions by polynomials, rational functions, splines entered in the theory of approximation more than 100 years ago and still retains its relevance. Among a large number of problems related to approximation, we considered the problem of polynomial approximation in two variables of a function defined on the continuum of an elliptic curve in C2 and holomorphic in its interior. The formulation of such a question led to the need to study the approximation of a function that is continuous on the continuum of the complex plane and analytic in its interior, using polynomials in doubly periodic Weierstrass functions and their derivatives. This work is devoted to the development of this topic.

Language: Russian

Full text

Text on another site

Approximation of the Effective Capacity for Multi-Server URLLC Systems With Batch Arrivals

Anton Karamyshev, Artem Krasilov, Evgeny Khorov, IEEE Transactions on Network Science and Engineering 2026 P. 1–18

Modern communication networks shall support mission-critical and real-time applications that demand high data rates, low latency, and ultra-high reliability, which is known as Ultra-reliable Low-latency Communications (URLLC). In URLLC systems, the effective capacity, i.e., the maximum traffic rate at which latency and reliability constraints are satisfied, is a key metric for resource management. Its estimations ...

Added: April 17, 2026

Constructive description of Holder classes on a chord-arc curve in R^3

Alexeeva T., Shirokov N. A., St Petersburg Mathematical Journal 2025 Vol. 36 No. 1 P. 25–39

Let L be a chord-arc curve in R3. We introduce a functional class Hr+ω(L) where a modulus of continuity ω satisfies the Dini condition and r≥1. We define neighborhoods of L Ωδ(L)=⋃M∈LBδ(M), Bδ(M)={X∈R3:∥XM∥<δ} and set HarmΩδ(L) for harmonic functions in Ωδ(L). The Theorem 1 states that if f∈Hω+r(L) then there exist functions vδ∈HarmΩδ(L) such that ∣∣f(X)−vδ(M)∣∣≤cfδrω(δ), M∈L, and ∣∣∂αvδ(M)∣∣≤cfω(δ)δ, M∈Ωδ(L), |α|=r+1. The Theorem 2 states that if a function f defined on L satisfies claim of Theorem 1 then f∈Hω+r(L). ...

Added: March 16, 2026

Целые функции экспоненциального типа в задаче приближения на дизъюнктных отрезках

Сильванович О. В., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2025 Т. 545 С. 179–205

Let ak < bk < ak+1, k ∈ Z, Ik = (ak, bk), Jk = [bk, ak+1]. We assume that |Ik| |Jk|, ak −−−−−→ k→+∞ ∞, ak −−−−−→ k→−∞ −∞ and |Jk| 1 |ak|α , |k| → ∞, α > 0. The distribution of {Jk} satisfies some regularity conditions, E = S k∈Z ...

Added: March 16, 2026

Мультипликативная полиномиальная аппроксимация

Медведев А. Н., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2025 № 545 С. 157–167

Let D be a bounded domain on the complex plain C with sufficiently smooth boundary. We denote by Λ αpDq, 0 α 1, the class of analytic functions in D satisfying the α-H¨older condition in D . Each function f P Λ αpDq can be factored as f F I with F ...

Added: March 16, 2026

Обобщение одной теоремы И. И. Привалова

Колпаков А. С., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2025 № 545 С. 145–156

Let E ⊂C be a compact set. The set E is called an Ahlfors–David set of dimension θ, 0 < θ < 2, if there exist constants C1, C2 > 0 such that for any z ∈ E and arbitrary r, 0 < r < diamE, one has C1rθ Λθ E∩Br(z) C2rθ, where Λθ(S) means ...

Added: March 15, 2026

Approximation of the Objective Function of Single-Machine Scheduling Problem

Alexander Lazarev, Nikolay Pravdivets, Barashov E., Mathematics 2024 Vol. 12 No. 5 Article 699

The problem of the approximation of the coefficients of the objective function of a scheduling problem for a single machine is considered. It is necessary to minimize the total weighted completion times of jobs with unknown weight coefficients when a set of problem instances with known optimal schedules is given. It is shown that the ...

Added: May 16, 2024

Приближение полиномами от двояко-периодических функций Вейерштрасса в LP метрике на дизъюнктных отрезках

Шагай М. А., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2023 Т. 527 С. 242–255

Let sk, 1 6 k 6 m, m > 2, be disjoint segments lying in a parallelogram Q. We denote by ℘(z) a doubly periodic Weierstrass function with the fundamental parallelogram Q. Let fk : sk → C be functions, and let f 0 k ∈ L pk (sk), 1 6 k 6 m, 1 ...

Added: February 10, 2024

Approximation by Polynomials Composed of Weierstrass Doubly Periodic Functions

Sintsova K. A., Shirokov N. A., Vestnik St. Petersburg University: Mathematics 2023 Vol. 56 No. 1 P. 46–56

The approximation-theory problem to describe classes of functions in terms of the rate of approximation of these functions by polynomials, rational functions, and splines arose over 100 years ago; it still remains topical. Among many problems related to approximation, we consider the two-variable polynomial approximation problem for a function defined on the continuum of an ...

Added: February 10, 2024

Конструктивное описание гёльдеровских пространств на chord-arc кривой в R^3

Alexeeva T., Shirokov N. A., Алгебра и анализ 2024 Т. 36 № 1 С. 40–59

On the chord-arc curve in R^3 classes of functions similar to Hölder functions with smoothness greater than unity are defined. A constructive description of these classes is obtained in terms of the rate of approximation of functions from them by functions that are harmonic in neighborhoods contracting to the curve. The choice of defining these classes ...

Added: January 10, 2024

О полилинейном функциональном уравнении

Illarionov A., Математические заметки 2020 Т. 107 № 1 С. 80–92

Решается функциональное уравнение, связанное с теоремами сложения и эллиптическими функциями ...

Added: November 15, 2023

On periodically modulated rolls in the generalized Swift–Hohenberg equation: Galerkin’ approximations

Kulagin N. E., L.M. Lerman, Physica D: Nonlinear Phenomena 2023 Vol. 454 Article 133845

We study in this pap er the existence of periodically modulated in one variable and localized in another variable solutions to the cubic Swift-Hohenberg equation on the plane R2. In the first part we try to apply the method by Kirschgassner-Mielke to reduce the problem to the search of finite-dimensional submanifolds with periodic orbits on them in some formal ...

Added: July 27, 2023

Algorithmization of Receiving Orbits of Weierstrass and Orbits of Tangences

Шагай М. А., Флегонтов А. В., Иофе М. Д., Springer 2021

In our paper we seek to find of constructive describe functional classes defined on subsets of the period's parallelogram of doubly periodic Weierstrass functions using the integral norm. ...

Added: February 6, 2023

Polynomially solvable subcases for the approximate solution of multi-machine scheduling problems

Alexander Lazarev, Lemtyuzhnikova D., Nikolay Pravdivets et al., , in: Advances in Optimization and Applications: 11th International Conference, OPTIMA 2020, Moscow, Russia, September 28 – October 2, 2020, Revised Selected PapersVol. 1340: Advances in Optimization and Applications.: Champaign: Springer Publishing Company, 2020. P. 211–223.

Added: December 16, 2022

A New Interpolation-Based Polynomial Algorithm for Estimating Lateness in Single Machine Scheduling Problem

Lazarev A. A., Lemtyuzhnikova D. V., Tyunyatkin A. A. et al., IFAC-PapersOnLine 2022 Vol. 55 No. 10 P. 2881–2886

This research extends the interpolation approach to approximating the objective function value for the minimization maximum lateness problem. The interpolation approach is defined using a special objective function Lmax(α), which is proven to be continuous and depends only on α transform coefficient. Such a function is proven to be monotonically increasing, and this property is ...

Added: December 5, 2022

Application of the Modified Method of S-Approximations within the Framework of the Structural-Parametric Approach for the Construction of Regional Analytical Models of the Magnetic Field of Mars

Salnikov A., Stepanova I., Gudkova T. et al., , in: 2021 14th International Conference Management of large-scale system development (MLSD).: IEEE, 2021. P. 1–3.

We have constructed an analytical model of the magnetic field over a region of the Martian surface using satellite raw data and S-approximations within the modified structural-parametric approach. The method mentioned above implies considering the environment features as a function included in an integral. We approximated the anomalous field by the sum of simple and ...

Added: October 30, 2022

Применение комбинированного подхода на основе аналитических аппроксимаций и построения интегральных кривых гравитационного поля для интерпретации морских и аэрогравиметрических данных

Степанова И. Э., Щепетилов А. В., Сальников А. М. et al., Наука и технологические разработки 2020 Т. 99 № 4 С. 34–52

Рассматривается развитие структурно-параметрического подхода к построению аналитических аппроксимаций. В рамках нового метода, включающего в себя модифицированные S-аппроксимации и нахождение интегральных кривых векторного поля, предложена методика нахождения аналитических продолжений поля в случае профильных (маршрутных) геофизических измерений. Приводятся результаты математического эксперимента с использованием реальных данных об аномальном гравитационном поле по результатам морской площадной гравиметрической съемки и аэрогравиметрической ...

Added: October 29, 2022

Arbitrarily accurate approximation of numerical characteristics of stationary ALOHA Channels

Burkov A. A., Shneer S., Turlikov A. M., , in: WAVE ELECTRONICS AND ITS APPLICATION IN INFORMATION AND TELECOMMUNICATION SYSTEMS. 2021. (WECONF 2021) St. Petersburg, Russia, 31 May - 4 June 2021.: IEEE, 2021. Ch. 9470700 P. 1–8.

The development of the Internet of Things technology in cellular networks is considered within the framework of massive machine-type communications with the use of random multiple access algorithms such as ALOHA and its modifications. Despite the fact that this class of algorithms has been studied for a long time, there are no numerical methods for ...

Added: October 28, 2022