On the well-posedness of multivariate spectrum approximation and convergence of high-resolution spectral estimators

In this paper, we establish the well-posedness of the generalized moment problems recently studied by Byrnes-Georgiou-Lindquist and coworkers, and by Ferrante-Pavon-Ramponi. We then apply these continuity results to prove almost sure convergence of a sequence of high-resolution spectral estimators indexed by the sample size. ∗Partially supported by the Ministry of Education, University, and Research of Italy (MIUR), under Project 2006094843: New techniques and applications of identification and adaptive control †Institut für Automatik, ETH Zürich, Physikstrasse 3, 8092 Zürich, Switzerland. email: [email protected] ‡Dipartimento di Ingeneria dell’Informazione, Università di Padova, via Gradenigo 6/B, I-35131 Padova, Italy. e-mail: [email protected] §Dipartimento di Matematica Pura e Applicata, Università di Padova, via Trieste 63, 35131 Padova, Italy. e-mail: [email protected] 1 ar X iv :0 91 1. 04 40 v1 [ m at h. O C ] 2 N ov 2 00 9