Asymptotic Behavior of Muntz Orthogonal Polynomials

作者：Stefansson Ulfar F^*

来源：Constructive Approximation, 2010, 32(2): 193-220.

DOI：10.1007/s00365-009-9059-x

• Muntz polynomials
• Muntz orthogonal polynomials

We provide a representation for the Muntz orthogonal polynomials as a real integral. This allows us to establish a general result on their asymptotic behavior within the interval of orthogonality. This is the first time that such asymptotics have been obtained for general Muntz exponents {lambda(n)}. We consider some special cases, particularly when the exponents satisfy the asymptotic relation
lim(n ->infinity) n/lambda(n) = rho
for some constant rho > 0.

• 出版日期2010-10