Asymptotic L₂ Inequalities of Markoff Type

Author: Shampine, Lawrence Fred

Year: 1964

Degree: Dissertation (Ph.D.)

Advisor: Todd, John

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/6W4R-N247

Abstract

The Markoff brothers have obtained bounds in the maximum norm for polynomials in terms of bounds for their derivatives. E. Schmidt has obtained asymptotic bounds for the analogous problem for weighted L[subscript 2] norms and the first derivative.

This thesis extends Schmidt's work in one case to the second derivative. A new technique is applied which recovers the principal term of Schmidt's asymptotic result and furnishes information about the extremal polynomials. Exact bounds are derived in one case.

Files

• Shampine_lf_1964.pdf (application/pdf)