Generalized hypergroups and orthogonal polynomials

Lasser, Rupert; Obermaier, Josef und Rauhut, Holger (2007): Generalized hypergroups and orthogonal polynomials. In: Journal of the Australian Mathematical Society, Vol. 82, No. 3: pp. 369-394

Abstract

The concept of semi-bounded generalized hypergroups (SBG hypergroups) is developed. These hypergroups are more special than generalized hypergroups introduced by Obata and Wildberger and more general than discrete hypergroups or even discrete signed hypergroups. The convolution of measures and functions is studied. In the case of commutativity we define the dual objects and prove some basic theorems of Fourier analysis. Furthermore, we investigate the relationship between orthogonal polynomials and generalized hypergroups. We discuss the Jacobi polynomials as an example.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Chair of Mathematics of Information Processing
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1446-7887
• Language: English