Friday, June 21, 2019 - 14:15 in V3-204
Periodic coordinates and a Magic Formula for Finite-gap CMV matrices
A talk in the Mathematik in den Naturwissenschaften series by
Benjamin Eichinger
| Abstract: |
We prove a bijective unitary correspondence between 1) the isospectral
torus of almost-periodic, absolutely continuous CMV matrices having
fixed finite-gap spectrum E and 2) periodic block-CMV matrices
satisfying a Magic Formula. This latter class arises as E-dependent
operator Moebius transforms of certain generating CMV matrices which are
periodic up to a rotational phase; for this reason we call them
``MCMV''.
Naturally, this has also consequences for the associated Schur
functions. We show that for any Schur function associated to a
finite-gap CMV matrix (and therefore with almost periodic Verblunsky
coefficients) there exists a more general Nevanlinna-Pick interpolation
problem with periodic interpolation data.
The talk is based on a joint work with J. S. Christiansen and T.
VandenBoom.
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