On factorization of biinfinite totally positive block Toeplitz matrices
Wolfgang Dahmen, Charles A. Micchelli, Philip W. Smith · Rocky Mountain Journal of Mathematics · 1986
We extend the work of Aissen, Schoenberg, Whitney, and Edrei, who characterized the symbol of a totally positive Toeplitz matrix, to characterizing the determinant of the symbol of a block Toeplitz totally positive matrix.As a consequence of our arguments we show that the symbol for the block Toeplitz case may be factored just as in the Toeplitz setting. Introduction.A biinfinite matrix A = 04,/), -oo < /, j < oo, is called totally positive provided that all its minors are nonnegative, i.e., for all ij n + m.In this case, we say A is m-banded.We will concentrate our attention here on matrices which are block Toeplitz.Thus for some integer N we require Aij = A i+NJ+N all /, j e Z.Any such matrix has the block structure (1.2) A = A-2 A"i A 0 A-2 A-x A 2 .