Some extensions and applications of dispersion relations

The rationale of dispersion relations (DR) is traced to von Neumann's "stat e properties" and is given a unifying formulation by the introduction of "e quations of restriction". Some questions surrounding reciprocal relations i n the time domain are discussed. Then, extensions of DR to multi-variable c ases are formulated through extended "equations of restrictions", which may be exact or approximate. These equations are applied to nonlocal dielectri cs (admitting of polariton modes), which are shown to obey (in general) lig ht-cone causality, though cases might occur in which a modification of the postulated dielectric functions is needed.