Functional equations in the theory of dynamic programming--IX: variational analysis, analytic continuation, and imbedding of operators.

by Richard Ernest Bellman, S. R. Lehman


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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.

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