STUDIES IN EIGENVALUE THEORY.
Final rept. 1 Jul 67-30 Jun 68,
AMERICAN UNIV WASHINGTON D C
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It was shown on a simple buckling problem that the method of Lagrangian multipliers, which was asssumed to be a simplification of the method of intermediate problems, actually yields incorrect numerical results. On the other hand, the method of intermediate problems provides simple and clear rules which are both mathematically rigorous and computationally feasible. A thorough study was made into the theoretical ramifications of intermediate problems. This investigation established the fact that intermediate problems, in addition to giving reliable lower bounds to eigenvalues, have stimulated research in purely theoretical subjects. Moreover, the contributions of intermediate problems to perturbation theory were clarified. The maximum-minimum and minimum-maximum principles for eigenvalues were extended to a class of unbounded operators of the type appearing in Schrodingers theory. The properties of projections of selfadjoint operators were investigated which led to some sufficient conditions for such operators to be selfadjoint. Conditions were established between the maximum-minimum and minimum-maximum principles which pointed out their complementary nature as well as some basic differences.
- Theoretical Mathematics