Distortion theorems for rational functions without poles or zeros in simply connected domains
(2000) Complex Variables: Theory and Application — Vol. 40, n° 4, p. 299-316 (2000)
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- Abstract
- We prove distortion theorems for rational functions without poles or zeros in simply connected domains. The distance between the values u(z 1) and u(z 2) assumed by such a rational function is limited by its degree and by the hyperbolic distance between z 1 and z 2. For discs and halfplanes, the case of equality in these estimates is fully explored. These results have appUcations in control theory which are illustrated by examples.
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Blondel, V., & Rupp, R. (2000). Distortion theorems for rational functions without poles or zeros in simply connected domains. Complex Variables: Theory and Application, 40(4), 299-316. https://doi.org/10.1080/17476930008815225 (Original work published 2000)