Positive Matrix Functions on the Bitorus with Prescribed Fourier Coefficients in a Band

M. Bakonyi, L. Rodman, I. M. Spitkovsky, H. J. Woerdeman

Research output: Contribution to journalArticlepeer-review

Abstract

Let S be a band in Z2 bordered by two parallel lines that are of equal distance to the origin. Given a positive definite ℓ1 sequence of matrices {cj}j∈S, we prove that there is a positive definite matrix function f in the Wiener algebra on the bitorus such that the Fourier coefficients f(k) equal ck for k ∈ S. A parameterization is obtained for the set of all positive extensions f of {cj}j∈S. We also prove that among all matrix functions with these properties, there exists a distinguished one that maximizes the entropy. A formula is given for this distinguished matrix function. The results are interpreted in the context of spectral estimation of ARMA processes.

Original languageEnglish (US)
Pages (from-to)20-44
Number of pages25
JournalJournal of Fourier Analysis and Applications
Volume5
Issue number1
DOIs
StatePublished - 1999

Keywords

  • ARMA processes
  • Almost periodic functions
  • Band method
  • Entropy
  • Matrix functions on bitorus
  • Positive extensions
  • Toeplitz operators
  • Wiener algebra

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Positive Matrix Functions on the Bitorus with Prescribed Fourier Coefficients in a Band'. Together they form a unique fingerprint.

Cite this