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Mathematics (Pomona)

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Complex symmetric operators, interpolation, self-adjoint extension, Takagi factorization, shift operators, inner functions, Darlington synthesis, Clark perturbations, Jordan operators, Volterra operators


We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, self-adjoint extensions of symmetric operators, rank-one unitary perturbations of the compressed shift, Darlington synthesis and matrix-valued inner functions, and free bounded analytic interpolation in the disk.


First published in Transactions of the American Mathematical Society in Volume 358, Number 3, 2005, published by the American Mathematical Society.

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© 2005 American Mathematical Society

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