Asymptotic L2 Inequalities of Markoff type

by Shampine, Lawrence Fred

Abstract (Summary)
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.
Bibliographical Information:

Advisor:John Todd

School:California Institute of Technology

School Location:USA - California

Source Type:Master's Thesis



Date of Publication:01/01/1964

© 2009 All Rights Reserved.