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Asymptotic L2 Inequalities of Markoff type


Shampine, Lawrence Fred (1964) Asymptotic L2 Inequalities of Markoff type. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/6W4R-N247.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Todd, John
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1964
Record Number:CaltechETD:etd-10042002-113549
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3892
Deposited By: Imported from ETD-db
Deposited On:07 Oct 2002
Last Modified:21 Dec 2019 03:04

Thesis Files

PDF (Shampine_lf_1964.pdf) - Final Version
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