[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2005.42.2.243

NEW RESULTS ABOUT ORTHOGONALITY PRESERVING MAPS

MARONI PASCAL (Laboratoire Jacques-Louis Lions Universite Pierre et Marie Curie-C.N.R.S.)

Publication Information

Journal of the Korean Mathematical Society / v.42, no.2, 2005 , pp. 243-254 More about this Journal

Abstract

The Alaway's theorem on orthogonality preserving maps [1] is revisited and we provide a new proof of this result, through an original separation property involving regular forms. In fact, we show a light more general result concerning weakly orthogonal sequences(see section 3).

Keywords

orthogonal polynomials; regular forms; isomorphisms;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
Times Cited By SCOPUS : 0

Reference

1	P. Maroni, Une caracterisation des polynomes orthogonaux semi-classiques, C. R. Acad. Sci. Paris Ser. I, 301 (1985), no. 6, 269-272
2	P. Maroni, Sur la suite de polynomes orthogonaux associee a la forme u = $\delta_c\;+\;\lambda(x-c)^{-1}L$ , Period. Math. Hung. 21 (1990), 223-248 DOI
3	P. Maroni, Une theorie algebrique des polynomes orthogonaux. Application aux polynomes orthogonaux semi-classiques, Ann. Comput. Appl. Math. 9 (1991), 95-130
4	P. Maroni, Variations around classical orthogonal polynomials. Connected problems J. Comput. Appl. Math. 48 (1993), 133-155 DOI ScienceOn
5	W. A. Al-Salam and A. Verma, Some orthogonality preserving operators, Proc. Amer. Math. Soc. 23 (1969), 136-139 DOI
6	W.A. Al-Salam and A. Verma, Orthogonality preserving operators, Accad. Naz. Lincei 58 (1975), 833-838
7	T. S. Chihara, An introduction to orthogonal polynomials, Gordon and Breach, New-York, 1978
8	W. R. Allaway, Orthogonality preserving maps and the Laguerre functional, Proc. Amer. Math. Soc. 100 (1987), 82-86