Cover: Functional equations in the theory of dynamic programming--IX

Functional equations in the theory of dynamic programming--IX

variational analysis, analytic continuation, and imbedding of operators

Published 1958

by Richard Ernest Bellman, S. R. Lehman

Purchase Print Copy

 Format Price
Add to Cart Paperback5 pages $15.00

An attempt to show how variational techniques can be applied to deduce properties (similar to those deduced from Green's function of various functional equations and properties of the resolvent operator) for complex and nonsymmetric operators. The study uses (1) a min-max variation and analytic continuation, if necessary, for complex operators and (2) an imbedding technique and analytic continuation, if required, for nonsymmetric operators. A nonsymmetric operator is imbedded within a family of symmetric operators associated with a variational problem. Once the variational problem is formulated, the functional-equation techniques of dynamic-programming theory are applied. 5 pp.

This report is part of the RAND paper series. The paper was a product of RAND from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.