Recursive properties of Toeplitz and Hurwitz matrices

AbstractBanded Toeplitz and Hurwitz matrices are shown to be particular cases of a more general class of biinfinite matrices, called recursive matrices. The main features of Toeplitz and Hurwitz matrices can thereby be seen to be immediate consequences of a fundamental theorem about recursive matrices, called the product rule. Moreover, some properties of products of Toeplitz and Hurwitz matrices can be proved by similar arguments. Some applications related to the general theory of compactly supported wavelets are presented