New results on stable multidimensional polynomials-Part I: Continuous case

New classes of multivariable polynomials arising in studies of passive multidimensional systems have been identified and their properties have been studied. In particular, polynomials occurring as the numerators and denominators of multivariable reactance functions and positive functions are characterized. Related properties of these and other classes of multivariable Hurwitz polynomials are also studied. Finally, a nontrivial test for the property of positivity of rational functions, holomorphic in a domain, in terms of their behavior on the distinguished boundary is formulated.