DUAL CONES, CONSTRAINED N-CONVEX L(P)-APPROXIMATION, AND PERFECT SPLINES

Authors
DEUTSCH F UBHAYA VA XU YS
Citation
F. Deutsch et al., DUAL CONES, CONSTRAINED N-CONVEX L(P)-APPROXIMATION, AND PERFECT SPLINES, Journal of approximation theory, 80(2), 1995, pp. 180-203
Citations number
37
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Journal of approximation theory → ACNP
ISSN journal
00219045
Volume
80
Issue
2
Year of publication
1995
Pages
180 - 203
Database
ISI
SICI code
0021-9045(1995)80:2<180:DCCNLA>2.0.ZU;2-S
Abstract
A generating basis and the dual cone of n-convex functions satisfying certain constraints are derived. As applications, the existence and ch aracterization of a best L(p)-approximation (1 less-than-or-equal-to p < infinity) from such subcones to a function in L(p) are established. The relationship between a best L1-approximation and perfect splines is developed under certain conditions. (C) 1995 Academic Press, Inc.