Abstract
The form of a Julia operator for a given Kreĭn space operator is determined when an invariant subspace and certain factorizations are known. The result is related to contractive triangular operator matrices and the Schur algorithm. In the context of one-step extension problems for power series, the method yields closed-form expressions for the centers and radii of disks which characterize interpolation. The main example is a coefficient interpolation problem for normalized Riemann mappings B(z) of the unit disk into itself. If B(z)v is expanded in powers z v, z v+1,. . . for any real v, then the n-th coefficient belongs to a closed disk whose center and radius depend on v and lower order coefficients.
Research supported by the National Science Foundation.
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To M. S. Livšic, with best wishes on his retirement.
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Christner, G., Li, K.Y., Rovnyak, J. (1994). Julia Operators and Coefficient Problems. In: Feintuch, A., Gohberg, I. (eds) Nonselfadjoint Operators and Related Topics. Operator Theory: Advances and Applications, vol 73. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8522-5_6
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