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math.FA2026
A Counterexample to the Gau--Wang--Wu Conjecture on Partial Isometries
Ryan O'Loughlin, Jani Virtanen
We disprove the conjecture of Gau, Wang and Wu that the numerical range of a finite-dimensional partial isometry, when circular, must be centred at the origin. More precisely, we p…
math.FA2024
A survey of asymptotics of determinants for structured matrices
E. Basor, T. Ehrhardt, J. A. Virtanen
In this survey we show how to produce asymptotics of determinants of structured matrices using operator theory methods. We describe the asymptotics for finite Toeplitz matrices, fi…
math.FA2024
Asymptotics of block Toeplitz determinants with piecewise continuous symbols
E. Basor, T. Ehrhardt, J. A. Virtanen
We determine the asymptotics of the block Toeplitz determinants as for matrix-valued piecewise continuous functions with a finitely man…