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A new property of Nevanlinna Functions
Tao Qian
2008
Conference Namethe 16th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
Source PublicationProceedings of the 16th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
Conference DateJuly 28–August 1, 2008
Conference PlaceDongguk University Gyeongju, Korea
Abstract

Writing the angular boundary limits (non-tangential boundary limits) of inner and outer functions in the unit disc in the form f(e it) = ρ(t)e iθ(t) , 0 ≤ t ≤ 2π, the paper studies the sign-change property of the “phase derivative” that reduces to θ 0 (t) if the function has an appropriate parameterization in t. We show in the inner functions case the Julia-Wolff-Carath´eodory Theorem may be rephrased to conclude the positivity property of the phase derivative. On the other hand, outer functions do not have such property. In the introduction we indicate that this study is motivated by the concept instantaneous frequency and relevant study in contemporary signal analysis.

KeywordInner Function Outer Function Blaschke Product Singular Inner Function Non-tangential Boundary Limit Angular Limit Angular Derivative Amplitude-phase Modulation Analytic Signal Instantaneous Frequency
Language英语
Fulltext Access
Document TypeConference paper
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
AffiliationDepartment of Mathematics University of Macau Macao (Via Hong Kong)
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Tao Qian. A new property of Nevanlinna Functions[C],2008.
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