Resumen de Conservative polynomial operators and discrete sobolev type products

F. J. Muñoz Delgado, Antonio Molina Alcalá

• In this work we study the existence of linear shape preserving polynomial operators of the form K(f) = Pn i=0 _i hf,QiiS Qi, where Qi are orthogonal polynomials with respect to the inner product hf, giS = R1 -1 f (x)g(x)dx + Mf0(c)g0(c) with M > 0 and c 2 [-1, 1]. We show some difficulties that appear when c 2 (-1, 1) and prove that for c = ±1 and for any k 2 {1, . . . , n} there exist values _i such that K|Pk = 1|Pk and K preserves the j-convexity for j 2 {k, . . . , n}.