Abstract
We consider an interpolation problem with n pairwise distinct nodes z 1,…,z n and n numbers w 1,…,w n, all on the unit circle in the complex plane, and seek interpolants b(z) of minimal degree in the class consisting of ratios of finite Blaschke products. The focus is on cases where the interpolant of minimal degree is uniquely determined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. G. Cantor and R. R. Phelps, An elementary interpolation theorem, Proc. Amer. Math. Soc. 16 (1965), 523–525.
C. Glader and G. Högnäs, An equioscillation characterization of finite Blaschke products, Complex Variables 42 2000) No.2, 107–118.
C. Glader and M. Lindström, Finite Blaschke product interpolation on the closed unit disc, J. Math. Anal. Appl. 273 2002) No.2, 417–427.
W. B. Jones and S. Ruscheweyh, Blaschke product interpolation and its application to the design of digital filters, Constr. Approx. 3 1987) No.4, 405–409.
G. Semmler and E. Wegert, Nonlinear Riemann-Hilbert problems and boundary interpolation, Comput. Methods Funct. Theory 3 2003) No.1, 179–199.
G. Semmler and E. Wegert, Boundary interpolation with Blaschke products of minimal degree, Comput. Methods Funct. Theory 6 2006) No.2, 493–511.
R. Younis, Interpolation by a finite Blaschke product, Proc. Amer. Math. Soc. 78 1980) No.3, 451–452.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Glader, C. Rational Unimodular Interpolation on the Unit Circle. Comput. Methods Funct. Theory 6, 481–492 (2006). https://doi.org/10.1007/BF03321625
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03321625