Stolze, JoachimBrandt, Uwe2008-06-032008-06-031981-03Brandt, Uwe; Stolze, Joachim: A new hierarchy of upper and lower bounds on expectation values. In: Zeitschrift für Physik B Nr. 1, Jg. 43(1981), S. 61-67 (1981), 10.1007/BF01295476.http://hdl.handle.net/2003/2541610.17877/DE290R-166Upper and lower bounds are constructed for expectation values of functions of a real random variable with derivatives up to orderN+1 which are alternately negative and positive over the whole range of interest. The bounds are given by quadrature formulas with weights and abscissas determined by the firstN+1 moments of the underlying probability distribution. Application to a simple disordered phonon system yields sharp bounds on the specific heat.enSpringer-Verlag51010.1007/BF01295476article (journal)