Abstract
We show how to construct all finite Blaschke product solution and the minimal scaled Blaschke product solution to the Nevanlinna-Pick interpolation problem in the open unit disc by solving eigenvalue problems of the interpolation data. Based on a result of Jones and Ruscheweyh we note that there always exists a finite Blaschke product of degree at most n - 1 that maps n distinct points in the closed unit disc, of which at least one is on the unit circle, into n arbitrary points in the closed unit disc, provided that the points inside the unit circle form a positive semi-definite Pick matrix of full rank. Finally, we discuss a numerical limiting procedure.
Original language | English |
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Pages (from-to) | 417-427 |
Number of pages | 11 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 273 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Sept 2002 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Finite Blaschke product
- Interpolation