On bilinear forms in Gaussian random variables and Toeplitz matrices

Matrix structures and applications

“…A similar property (Avram-Parter theorem [6], [63]) holds for singular values. The requirement that f (x) is in L ∞ given in the original result of [63] has been relaxed by Tyrtyshnikov [74].…”

“…That is, it is very likely that no digit is correct in the computed estimate of |x n |. This fact is clearly shown in Figure 1 where the values of log 10 |p The values of log 10 |p (6) i | for i = 0, . .…”

Asymptotic properties of parameter estimates for random fields with tapered data

“…Theorem A.1 is a generalization of the statements (C) of Theorem 4.7 in [25] (see also [9]) to the case of fields (in Z d ) and for tapered data. For the case of Gaussian processes with discrete time, and spectral densities with possible singularities, the following results were obtained in [24] (without tapering, that is, h(t) ≡ 1).…”

Szegö Type Results Relative to a Sequence of Model Spaces

“…We shall use the L 2 version [8] of the classical Szegö theorem and the theorem of Avram [1] and Parter [5] concerning the singular values. We can find demonstrations in the continuous case using the operator theory and the C * -algebras in [2].…”