FINITE FREQUENCY-RANGE KRAMERS-KRONIG RELATIONS - BOUNDS ON THE DISPERSION

Dispersion inequalities are presented to check for the self-consistenc y of experimentally obtained complex moduli, such as the complex diele ctric constant, magnetic permeability, and complex bulk and shear modu li of viscoelastic materials. Unlike the Kramers-Kronig dispersion rel ations, they only require measurements over a finite frequency range. They can provide highly accurate interpolation formulas for the real p art, given its value at a few selected frequencies and given the imagi nary part over a range of frequencies.