TL;DR
This paper extends Szego limit theorems to more general measures, determinants, and higher dimensions, broadening their applicability in Toeplitz matrix analysis.
Contribution
It introduces new generalizations of Szego limit theorems, including higher-dimensional extensions and broader measure and determinant classes.
Findings
Extended Szego limit theorems to more general measures
Generalized determinants in Toeplitz matrices
Developed higher-dimensional Szego limit results
Abstract
The first Szego limit theorem has been extended by Bump-Diaconis and Tracy-Widom to limits of other minors of Toeplitz matrices. We extend their results still further to allow more general measures and more general determinants. We also give a new extension to higher dimensions, which extends a theorem of Helson and Lowdenslager.
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Taxonomy
TopicsRandom Matrices and Applications · Advanced Topics in Algebra · Advanced Algebra and Geometry