Two Linear Transformations each Tridiagonal with Respect to an Eigenbasis of the other; Comments on the Parameter Array

PAUL TERWILLIGER

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Two Linear Transformations each Tridiagonal with Respect to an Eigenbasis of the other; Comments on the Parameter Array

机译：关于彼此的本征基础的两个线性变换，每个都是三对角的；关于参数数组的注释

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摘要

We display all the parameter arrays in parametric form. For each array we compute the above polynomials. The resulting polynomials form a class consisting of the q-Racah, q-Hahn, dual q-Hahn, q-Krawtchouk, dual q-Krawtchouk, quantum q-Krawtchouk, affine q-Krawtchouk, Racah, Hahn, dual-Hahn, Krawtchouk, Bannai/Ito, and Orphan polynomials. The Bannai/Ito polynomials can be obtained from the q-Racah polynomials by letting q tend to -1. The Orphan polynomials have maximal degree 3 and exist for char(K) = 2 only. For each of the polynomials listed above we give the orthogonality, 3-term recurrence, and difference equation in terms of the parameter array.

机译：我们以参数形式显示所有参数数组。对于每个数组，我们计算上述多项式。所得多项式形成一个由q-Racah，q-Hahn，对偶q-Hahn，q-Krawtchouk，对偶q-Krawtchouk，量子q-Krawtchouk，仿射q-Krawtchouk，Racah，Hahn，对偶-Hahn，Krawtchouk组成的类，Bannai / Ito和孤立多项式。通过让q趋于-1，可以从q-Racah多项式获得Bannai / Ito多项式。孤立多项式的阶数最大为3，并且仅在char（K）= 2时才存在。对于上面列出的每个多项式，我们根据参数数组给出正交性，3项递归和差分方程。

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来源
《Designs, Codes and Crytography》 |2005年第3期|p.307-332|共26页
作者
PAUL TERWILLIGER;
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作者单位

Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706, USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类高等数学;
关键词
leonard pair; tridiagonal pair; askey-wilson polynomial; q-racah polynomial;

机译：leonard对;对角对对;askey-wilson多项式;q-racah多项式;

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专利

1. Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition [J] . Terwilliger P Journal of Computational and Applied Mathematics . 2005,第1a2期

机译：两个线性变换，每个线性变换相对于另一个特征本征是三对角的：关于分解的评论
2. Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form [J] . Terwilliger P Journal of Algebra . 2005,第1期

机译：两个线性变换，每个线性变换相对于彼此的本征为三对角线; TD-D规范形式和LB-UB规范形式
3. Two linear transformations each tridiagonal with respect to an eigenbasis of the other [J] . Terwilliger P. Linear Algebra and its Applications . 2001,第1a3期

机译：两个线性变换，每个线性变换相对于另一个的本征基
4. Image enhancement method for underwater images based on discrete cosine eigenbasis transformation [C] . Tatsuya Baba, Keishu Nakamura, Seisuke Kyochi, IEEE International Conference on Image Processing . 2017

机译：基于离散余弦本征基变换的水下图像图像增强方法
5. On an eigenvalue problem for some nonlinear transformations of multi-dimensional arrays. [D] . Kaur, Sawinder Pal. 2007

机译：关于多维数组的某些非线性变换的一个特征值问题。
6. Representation of One-Parameter Semi-Groups of Linear Transformations [O] . Einar Hille 1942

机译：线性变换的一参数半群的表示
7. Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array [O] . Terwilliger, Paul 2003

机译：两个线性变换，每个线性变换相对于一个三对角线另一个的本征基础;对参数数组的注释
8. USE OF TRANSFORMATIONS ON PARAMETERS IN NON-LINEAR THEORY. Ⅱ. MEASURES OF NON-LINEARITY AND TRANSFORMATIONS TO REDUCE NON-LINEARITY [R] . Irwin Guttman, Duane A. Meeter 1964

机译：变换在非线性理论中对参数的应用。 Ⅱ。非线性和变换的措施，以减少非线性

Two Linear Transformations each Tridiagonal with Respect to an Eigenbasis of the other; Comments on the Parameter Array

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