Factorization of totally positive, symmetric, periodic, banded matrices with applications (Q1208284)

The paper contains the following result: --- A totally positive, symmetric, periodic, banded matrix \(A\) can be factored in a symmetric manner into positive one-banded periodic factors, and, as a deduction from this result, \(A\) has positive eigenvalues with certain restrictions on their coincidence and on the sign changes of the corresponding eigenvectors. The spectral properties of certain positive, periodic spline operators are also derived.