Shampine, Lawrence Fred (1964) Asymptotic L2 Inequalities of Markoff type. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-10042002-113549
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|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||1 January 1964|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||07 Oct 2002|
|Last Modified:||26 Dec 2012 03:03|
- Final Version
See Usage Policy.
Repository Staff Only: item control page