Approximation in weighted spaces of vector functions

Authors : Gavriil PALTINEANU, Ileana BUCUR

Pages : 242-252

Doi:10.33205/cma.825986

View : 15 | Download : 9

Publication Date : 2021-06-01

Article Type : Research Paper

Abstract :In this paper, we present the duality theory for general weighted space of vector functions. We mention that a characterization of the dual of a weighted space of vector functions in the particular case $V \subset C^{+} insert ignore into journalissuearticles values(X);$ is mentioned by J. B. Prolla in [6]. Also, we extend de Branges lemma in this new setting for convex cones of a weighted spaces of vector functions insert ignore into journalissuearticles values(Theorem 4.2);. Using this theorem, we find various approximations results for weighted spaces of vector functions: Theorems 4.2-4.6 as well as Corollary 4.3. We mention also that a brief version of this paper, in the particular case $V \subset C^{+} insert ignore into journalissuearticles values(X);$, is presented in [3], Chapter 2, subparagraph 2.5.
Keywords : Nachbin family, weighted space, antialgebraic set