- 期刊
ASYMPTOTIC TRACTS OF HARMONIC FUNCTIONS III
摘要
A tract (or asymptotic tract) of a real function u harmonic and nonconstant in the complex plane C is one of the n_c components of the set {z:u(z)≠c}, and the order of a tract is the number of non-homotopic curves from any given point to ∞ in the tract. The authors prove that if u(z) is an entire harmonic polynomial of degree n, if the critical points of any of its analytic completions f lie on the level sets τ_□={z:u(z)=c_□}, where 1≤ □ ≤p and p ≤ n-1, and if the total order of all the critical points of f on τ_□ is denoted by σ_j, then (The equation is abbreviated).
延伸閱讀
- SCHMIDT, A. U. (2005). ASYMPTOTIC HYPERFUNCTIONS, TEMPERED HYPERFUNCTIONS, AND ASYMPTOTIC EXPANSIONS. International Journal of Mathematics and Mathematical Sciences, 2005(), 755-788-057. https://doi.org/10.1155/IJMMS.2005.755
- 蘇哲寬（2019）。Asymptotic behavior on Laplace Transform〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU201901693
- Chan, L. Y. (1978). Some approximation theorems for asymptotic functions [master's thesis, The University of Hong Kong]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0029-1812201200005265
- Cattani, C., & Kudreyko, A. (2008). On the Discrete Harmonic Wavelet Transform. Mathematical Problems in Engineering, 2008(), 1006-1012. https://doi.org/10.1155/2008/687318
- Wang, Y. Z. (2013). Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation. Journal of Applied Mathematics, 2013(), 470-477-252. https://doi.org/10.1155/2013/353757