Introduction. The trigonometric moment problem stands at the source of several major streams in analysis. From it flow developments in function theory, in spectral representation of operators, in probability, in approximation, and in the study of inverse problems. Here we connect it also with a group of questions centering on entropy and prediction. In turn, this will suggest a simple approach,...

For a large class of linear neutral-type systems the problem of assigning eigenvalues and eigenvectors is investigated, i.e. finding the system that has the given spectrum and, in some sense, allmost all eigenvectors. The solution of this problem enables vector moment problems to be considered using the construction of a neutral-type system. The exact controllability property of the system obta...

This paper is dedicated to Arthur Krener – a great researcher, a great teacher and a great friend – on the occasion of his 60th birthday. In this work we study the generalized moment problem with complexity constraints in the case where the actual values of the moments are uncertain. For example, in spectral estimation the moments correspond to estimates of covariance lags computed from a finit...

The rational covariance extension problem (RCEP) is an important problem in systems and control occurring in such diverse fields as control, estimation, system identification, and signal and image processing, leading to many fundamental theoretical questions. In fact, this inverse problem is a key component in many identification and signal processing techniques and plays a fundamental role in ...

We give a general framework of statistical aspects of the problem of understanding and a description of image symmetries, by utilizing the theory of moment invariants. In particular, we examine the issues of joint symmetry estimation and detection. These questions are formulated as the statistical decision and estimation problems since we cope with images observed in the presence of noise. The ...

Let A(G) be the adjacency matrix of a graph G with λ1(G), λ2(G), . . . , λn(G) its eigenvalues in non-increasing order. Call the number Sk(G) := ∑ n i=1 λ i (G) (k = 0, 1, . . . , n − 1) the kth spectral moment of G. Let S(G) = (S0(G), S1(G), . . . , Sn−1(G)) be the sequence of spectral moments of G. For two graphsG1 and G2, we have G1 ≺s G2 if Si(G1) = Si(G2) for i = 0, 1, . . . , k−1 and Sk(G...

In the field of orthogonal polynomials theory, the classical Markov theorem shows that for determinate moment problems the spectral measure is under control of the polynomials asymptotics. The situation is completely different for indeterminate moment problems, in which case the interesting spectral measures are to be constructed using Nevanlinna theory. Nevertheless it is interesting to observ...

Let Ln,t be the set of all n-vertex connected graphs with clique number t (2 ≤ t ≤ n). For nvertex connected graphs with given clique number, lexicographic ordering by spectral moments (S-order) is discussed in this paper. The first ∑⌊(n−t−1)/3⌋ i=1 (n − t − 3i) + 1 graphs with 3 ≤ t ≤ n − 4, and the last few graphs, in the Sorder, among Ln,t are characterized. In addition, all graphs in Ln,n ∪...

We have developed and implemented an automated moment tensor inversion procedure to determine source parameters for southern California earthquakes. The method is based upon spectral-element simulations of regional seismic wave propagation in an integrated 3D southern California velocity model. Sensitivity to source parameters is determined by numerically calculating the Fréchet derivatives req...

We have studied solar variations during the Holocene (i.e. last ~11,700 yr) by combining a new model of the Earth’s dipole moment with C data from the IntCal04 record and Be data from the GRIP ice core. Joint spectral analysis of the two nuclide records suggests that the periodic behavior of the Sun was particularly pronounced between 6000-4500 yr BP and 3000-2000 yr BP, with dominating periodi...