Corresponding Banach spaces on time scales

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:179

Article; Proceedings Paper

Ruffing, A ; Simon, M

关键词: Banach space;    time scale;    positively regressive;    cylinder transform;    isometry;   

DOI  :  10.1016/j.cam.2004.09.047

来源: Elsevier

【 摘 要 】

We will provide a short introduction to the calculus on a time scale T, in order to make the reader familiar with the basics. Then we intend to have a closer look at the so-called cylinder transform xi(mu) which maps a positively regressive function p : T -> R to another function p : T -> R. It will turn out that, under certain conditions, this cylinder transform acts as art isometry between two normed spaces. Therefore, we obtain a two-fold generalization of the well-known Banach and Hilbert spaces of functions in continuum analysis. Finally, we shall give some examples concerning this structure of corresponding spaces-for instance an example of orthogonal polynomials on equidistant lattices. In order to achieve this, we shall state a theorem on how to take orthogonality theory over from a Hilbert space to its corresponding Hilbert space. (c) 2004 Elsevier B.V. All fights reserved.

【 授权许可】

Free