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Boundary derivatives of the phases of inner and outer functions and applications |
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| Authors: | Tao Qian |
| Affiliation: | Department of Mathematics, University of Macau, Macao (Via Hong Kong), Macau |
| Abstract: | We prove that boundary derivatives of the phases of inner functions exist and are positive almost everywhere, but those of outer functions, on the other hand, have zero mean on the boundary. The concepts and results have definitive applications to the definitions of instantaneous frequency and mono‐components complying with requirements in physics and contemporary study of analytic signals. Copyright © 2008 John Wiley & Sons, Ltd. |
| Keywords: | inner function outer function Blaschke product singular inner function non‐tangential boundary limit angular limit angular derivative amplitude– phase modulation analytic signal instantaneous frequency |