Diagonalizability and symmetrizability of Sobolev-type bilinear forms: A combinatorial approach

被引：3

作者：

Kim, H. K. ^{[1
]}

Kwon, K. H. ^{[2
]}

Littlejohn, L. L. ^{[3
]}

Yoon, G. J. ^{[4
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[2] Korea Adv Inst Sci & Technol, Dept Math Sci, Taejon 305701, South Korea

[3] Baylor Univ, Dept Math, Waco, TX 76798 USA

[4] Ewha W Univ, Inst Math Sci, Seoul 120750, South Korea

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 460卷

基金：

新加坡国家研究基金会;

关键词：

Sobolev-type bilinear form; Diagonalizability; Symmetrizability; MOMENT PROBLEM; ORTHOGONAL POLYNOMIALS;

D O I：

10.1016/j.laa.2014.07.037

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In an earlier paper, Kwon, Littlejohn and Yoon characterized symmetric Sobolev bilinear forms and showed that they have, like symmetric matrices, a diagonal representation. In this paper, we present a new proof of one of their main results by interpreting the coefficients in the diagonal representation of a Sobolev-type bilinear form from a combinatorial point of view. We view this as an improvement over the original proof which relied on mathematical induction. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：111 / 124

页数：14

共 18 条

[1]

Alvarez M., 1996, LECT NOTES PURE APPL, V199, P343

[2]

[Anonymous], 2004, NUMER MATH SCI COMPU

[3]

Blankenagel J., 1971, THESIS U KOLN

[4]

Boas Jr RP., 1939, Bull Am Math Soc, V45, P399, DOI DOI 10.1090/BULL/1939-45-06

[5]

Chihara Theodore S, 2011, An introduction to orthogonal polynomials

[6]

Danese A.E., 1976, REND SEM MAT U POLIT, V35, P1

[7] THE STIELTJES MOMENTS PROBLEM FOR RAPIDLY DECREASING FUNCTIONS [J].

DURAN, AJ .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 107 (03) :731-741

[8] Ghost matrices and a characterization of symmetric Sobolev bilinear forms [J].

Kwon, K. H. ;

Littlejohn, Lance L. ;

Yoon, G. J. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (1-2) :104-119

[9] Sobolev orthogonal polynomials and second-order differential equations [J].

Kwon, KH ;

Littlejohn, LL .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1998, 28 (02) :547-594

[10]

Lay D.C., 2003, Linear Algebra and Its Applications

← 1 2 →