Discrete Invariant Curve Flows, Orthogonal Polynomials, and Moving Frame

被引：1

作者：

Wang, Bao ^{[1
,2
,3
]}

Chang, Xiang-Ke ^{[1
,2
]}

Hu, Xing-Biao ^{[1
,2
]}

Li, Shi-Hao ^{[1
,2
,4
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, POB 2719, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[3] Brock Univ, Dept Math & Stat, St Catharines, ON L2S 3A1, Canada

[4] Univ Melbourne, Sch Math & Stat, Melbourne, Vic 3010, Australia

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2021年 / 2021卷 / 14期

基金：

中国国家自然科学基金;

关键词：

DIFFERENTIAL INVARIANTS; DYNAMICS; GEOMETRY; COFRAMES; SOLITON;

D O I：

10.1093/imrn/rnz379

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, an orthogonal polynomials-based (OPs-based) approach to generate discrete moving frames and invariants is developed. It is shown that OPs can provide explicit expressions for the discrete moving frame as well as the associated difference invariants, and this approach enables one to obtain the corresponding discrete invariant curve flows simultaneously. Several examples in the cases of centro-affine plane, pseudo-Euclidean plane, and high-dimensional centro-affine space are presented.

引用

页码：11050 / 11092

页数：43

共 50 条

[1] Smoothing curve by orthogonal polynomials
Pansomboon, Sukpak
Rattanathanawan, Pongpan
Podisuk, Maitree
[J]. PROCEEDINGS OF THE 15TH AMERICAN CONFERENCE ON APPLIED MATHEMATICS AND PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON COMPUTATIONAL AND INFORMATION SCIENCES 2009, VOLS I AND II, 2009, : 225 - +
[2] POLYNOMIALS ORTHOGONAL OVER A CURVE
DUREN, PL
[J]. MICHIGAN MATHEMATICAL JOURNAL, 1965, 12 (03) : 313 - &
[3] Invariant discrete flows
Benson, Joseph
Valiquette, Francis
[J]. STUDIES IN APPLIED MATHEMATICS, 2019, 143 (01) : 81 - 119
[4] On zeros of discrete orthogonal polynomials
Krasikov, Ilia
Zarkh, Alexander
[J]. JOURNAL OF APPROXIMATION THEORY, 2009, 156 (02) : 121 - 141
[5] Discrete Entropies of Orthogonal Polynomials
Aptekarev, A. I.
Dehesa, J. S.
Martinez-Finkelshtein, A.
Yanez, R.
[J]. CONSTRUCTIVE APPROXIMATION, 2009, 30 (01) : 93 - 119
[6] Discrete orthogonal matrix polynomialsДискретные ортогональные матричные полиномы
Raúl Felipe
[J]. Analysis Mathematica, 2009, 35 (3) : 189 - 197
[7] Discrete classical orthogonal polynomials
Kwon, KH
Lee, DW
Park, SB
Yoo, BH
[J]. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 1998, 4 (02) : 145 - 162
[8] Discrete Entropies of Orthogonal Polynomials
A. I. Aptekarev
J. S. Dehesa
A. Martínez-Finkelshtein
R. Yáñez
[J]. Constructive Approximation, 2009, 30 : 93 - 119
[9] Discrete orthogonal matrix polynomials
Felipe, Raul
[J]. ANALYSIS MATHEMATICA, 2009, 35 (03) : 189 - 197
[10] Orthogonal Polynomials on a Planar Quartic Curve
Phung Van Manh
[J]. Mediterranean Journal of Mathematics, 2024, 21

← 1 2 3 4 5 →