Abstract
Variational calculations in Hilbert space and theorems from the Tchebycheff-Stieltjes-Markoff moment theory are employed in the construction of Stieltjes-integral approximations to a number of elementary dispersion relations. Appropriate derivatives of the Stieltjes integrating functions provide convergent estimates for the absorptive and dispersive conjugate functions in their nonanalytic regions on the real axis, where the dispersion relations are of particular interest. Illustrative applications are given in the cases of the Kramers-Kronig-Heisenberg dispersion formula, the closely related wave number-dependent dielectric response function, a dispersion relation that arises in connection with lattice vibrations and the thermodynamic properties of crystals, and the Schwinger-Baker formula for the elastic-scattering Fredholm determinant.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
