Markov-Type Inequalities for Products of Müntz Polynomials

Abstract

Let @[email protected]?(@l"j)^~"j"="0 be a sequence of distinct real numbers. The span of {x^@l^"^0, x^@l^"^1, ..., x^@l^"^n} over R is denoted by M"n(@L)@?span{x^@l^"^0, x^@l^"^1, ..., x^@l^"^n}. Elements of M"n(@L) are called Muntz polynomials. The principal result of this paper is the following Markov-type inequality for products of Muntz polynomials. [email protected]@?(@l"j)^~"j"="[email protected]@?(@c"j)^~"j"="0be increasing sequences of nonnegative real numbers. LetK(M"n(@L), M"m(@C))@[email protected]?x(pq)'(x)@?"["0"," "1"]@[email protected]?"["0"," "1"]:[email protected]?M"n(@L),[email protected]?M"m(@C).Then13((m+1)@l"n+(n+1)@c"m)=