FUNCTIONAL EQUATIONS IN THE THEORY OF DYNAMIC PROGRAMMING. IX. VARIATIONAL ANALYSIS, ANALYTIC CONTINUATION, AND IMBEDDING OF OPERATORS
RAND CORP SANTA MONICA CA
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In this paper it is shown how variational techniques can be applied to deduce properties for complex operators and for operators which are non- symmetric. For complex operators use is made of a min-max variation and analytic continuation, if necessary, while for non-symmetric operators an imbedding technique was used, along with analytic continuation when required. A non-symmetric operator is imbedded within a family of symmetric operators associated with a variational problem. Once the variational problem has been formulated one can apply the functional equation techniques of the theory of dynamic programming.
- Theoretical Mathematics