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The authors generalize a method of Lehmann and Maehly for upp er and lower bounds to eigen valu es of selfadjoint operators in Hilbert space by using a device introduced by Kato. The res ulting procedure ca n be used to improve bounds found by th e RayleighRitz me thod and the comparison me thods of We in stein, Aronszajn, and the authors by mean s of calculati ons involving easily found vectors; and it is es pec ially suitabl e for applicat ion to probl e ms of vibratio n of co ntinuou s elasti c s yste ms. Further a th eore m of Kato is inte rpre ted and ext e nd ed by th e res ult s obtained.
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Bazley et al. (1964) studied this question.
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