BernsteinType Inequalities for Linear Combinations of Shifted Gaussians Academic Article

abstract

• Let Pn be the collection of all polynomials of degree at most n with real coefficients. A subtle Bernstein-type extremal problem is solved by establishing the inequality Un(m)| Lq() (c1+1/qm)m/2 n m/2UnLq() for all U n Gn, q (0, ], and m = 1, 2,..., where c is an absolute constant and Gn := {f : f(t) = j=1N Pmj (t)e-(t-j)2, j , Pmj, j=1N (mj + 1) n}. Some related inequalities and direct and inverse theorems about the approximation by elements of Gn in Lq() are also discussed. 2006 London Mathematical Society.

authors

• Erdelyi, Tamas

published proceedings

• Bulletin of the London Mathematical Society

author list (cited authors)

• Erdlyi, T.

citation count

• 6

complete list of authors

• Erdélyi, Tamás

publication date

• February 2006

publisher

• Wiley  Publisher

published in

• Bulletin of the London Mathematical Society  Journal

keywords

• 10 Reduced Inequalities
• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1112/s0024609305018035

start page

• 124

end page

• 138

volume

• 38

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1112%2Fs0024609305018035

user-defined tag

• 10 Reduced Inequalities