RT Journal Article
T1 Unconditional constants and polynomial inequalities
A1 Grecu, B.C.
A1 Muñoz-Fernández, Gustavo A.
A1 Seoane Sepúlveda, Juan Benigno
AB If P is a polynomial on R of degree at most n, given by P(x) = Sigma(alpha is an element of Nm,vertical bar alpha vertical bar <= n) a(alpha)x(alpha), and P(n)(R(m)) is the space of such polynomials, then we define the polynomial vertical bar P vertical bar by vertical bar P vertical bar(x) = Sigma(alpha is an element of Nm,vertical bar alpha vertical bar <= n) vertical bar a(alpha vertical bar)x(alpha). Now if B subset of R(m) is a convex set, we define the norm parallel to P parallel to(B) := sup{vertical bar(x)vertical bar : x is an element of B} on P(n)(R(m)), and then we investigate the inequality vertical bar vertical bar vertical bar P vertical bar vertical bar vertical bar(B) <= C(B)vertical bar vertical bar vertical bar P vertical bar vertical bar vertical bar(B), providing sharp estimates on C(B) for some specific spaces of polynomials. These C(B)'s happen to be the unconditional constants of the canonical bases of the considered spaces.
PB Academic Press- Elsevier Science
SN 0021-9045
YR 2009
FD 2009-12
LK https://hdl.handle.net/20.500.14352/42379
UL https://hdl.handle.net/20.500.14352/42379
LA eng
NO Marie Curie Intra European Fellowship
NO Spanish Ministry of Education
DS Docta Complutense
RD 9 abr 2025