Characterizations of Mono-Components: the Blaschke and Starlike Types | |
Qian, Tao1; Tan, Lihui2 | |
2018-08 | |
Source Publication | COMPLEX ANALYSIS AND OPERATOR THEORY |
ISSN | 1661-8254 |
Volume | 12Issue:6Pages:1383-1399 |
Abstract | 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. |
Keyword | Circular Analytic Signal Mono-component Blaschke Product Bedrosian Identity Multivalent Starlike Functions Boundary Starlike Functions |
DOI | http://doi.org/10.1007/s11785-015-0491-6 |
URL | View the original |
Indexed By | SCI |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000439367300001 |
Publisher | SPRINGER BASEL AG |
The Source to Article | WOS |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Corresponding Author | Qian, Tao; Tan, Lihui |
Affiliation | 1.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 Affilication | Faculty of Science and Technology |
Corresponding Author Affilication | Faculty of Science and Technology |
Recommended Citation 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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