Characterizations of Mono-Components: the Blaschke and Starlike Types
Qian, Tao1; Tan, Lihui2

Since the last decade, motivated by attempts of positive frequency decomposition of signals, complex periodic functions s(ei t) =.(t) ei.(t) satisfying the conditions H(.(t) cos.(t)) =.(t) sin.(t),.(t) = 0,. (t) = 0, a. e., have been sought, where H is the circular Hilbert transform and the phase derivative. (t) is suitably defined and interpreted as instantaneous frequency of the signal.(t) cos.(t). Functions satisfying the above conditions are called mono-components. Mono-components have been found to form a large pool and used to decompose and analyze signals. This note in a great extent concludes the study of seeking for monocomponents through characterizing two classes of mono-components of which one is phrased as the Blaschke type and the other the starlike type. The Blaschke type mono- components are of the form.(t) cos.(t), where.(t) is a real- valued (generalized) amplitude functions and ei.(t) is the boundary limit of a finite or infinite Blaschke product. For the starlike type mono- components, we assume the condition 2p 0. (t) dt = np, where n is a positive integer. It shows that such class of monocomponents is identical with the class consisting of products between p- starlike and boundary (n - 2p)- starlike functions. The results of this paper explore connections between harmonic analysis, complex analysis, and signal analysis.

KeywordCircular Analytic Signal Mono-component Blaschke Product Bedrosian Identity Multivalent Starlike Functions Boundary Starlike Functions
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Indexed BySCI
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000439367300001
The Source to ArticleWOS
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorQian, Tao; Tan, Lihui
Affiliation1.Faculty of Science and Technology, University of Macau, Taipa, Macau, China
2.School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, People’s Republic of China
First Author AffilicationFaculty of Science and Technology
Corresponding Author AffilicationFaculty of Science and Technology
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GB/T 7714
Qian, Tao,Tan, Lihui. Characterizations of Mono-Components: the Blaschke and Starlike Types[J]. COMPLEX ANALYSIS AND OPERATOR THEORY,2018,12(6):1383-1399.
APA Qian, Tao,&Tan, Lihui.(2018).Characterizations of Mono-Components: the Blaschke and Starlike Types.COMPLEX ANALYSIS AND OPERATOR THEORY,12(6),1383-1399.
MLA Qian, Tao,et al."Characterizations of Mono-Components: the Blaschke and Starlike Types".COMPLEX ANALYSIS AND OPERATOR THEORY 12.6(2018):1383-1399.
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