The orthogonal polynomials for a linear sum of a free family of projections

被引：5

作者：

Akiyama, M

Yoshida, H

机构：

[1] Ochanomizu Univ, Dept Math, Bunkyo Ku, Tokyo 112, Japan

[2] Ochanomizu Univ, Dept Informat Sci, Bunkyo Ku, Tokyo 112, Japan

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 1999年 / 2卷 / 04期

关键词：

D O I：

10.1142/S0219025799000357

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We calculate the probability measures for some linear combinations of a free family of projections by using Voiculescu's R-transform for free additive convolution in the free probability theory. The measures we give in this paper include many examples that have been calculated, for instance, the spectral measure for the adjacency operators of the infinite distance regular graphs, and the Plancherel measures associated with free product groups. Furthermore, we find the recursive relations for the orthogonal polynomials associated with them.

引用

页码：627 / 643

页数：17

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