Abstract:For an inhomogeneous string with known mass distribution (the total mass is assumed to be infinite), known finite length, and unknown spectral measure d t σ( ) , we construct an analogous string with spectral measure d t t σ( ) / . This enables one to determine the moments of all nonnegative orders for the measure d t σ( ). The mechanical interpretation of Stieltjes' investigation of the problem of moments proposed by Krein enables one to solve the problem of finding the moments of negative orders for the Stie… Show more
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