Extremal properties of the derivatives of the Newman polynomials Conference Paper uri icon

abstract

  • Let n-1 := {1, 2, . . ., n} be a set of n distinct positive numbers. The span of {e-1t, e-2t, . . ., e -nt} over R will be denoted by E(n-1) := span{e-1t, e-2t, . . ., e -nt}. Our main result of this note is the following. Theorem. Suppose 0 < q p . Let be a non-negative integer. Then there are constants c1(p, q, ) > 0 and c2(p, q, ) > 0 depending only on p, q, and such that c1(p, q, ) (j=1n j) +1/q-1/p supQE(n-1) Q ()Lp [0,)/QLg [0,) c2(p, q, ) (j=1n j)+1/q-1/p where the lower bound holds for all 0 < q p and for all 0, while the upper bound holds when = 0 and 0 < q p and when 1, p 1, and 0 < q p .

published proceedings

  • PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

author list (cited authors)

  • Erdelyi, T.

citation count

  • 9

complete list of authors

  • Erdelyi, T

publication date

  • February 2003