On asymptotic behavior of fractional Cauchy transform
Sign Up to like & getrecommendations! Published in 2019 at "Analysis and Mathematical Physics"
DOI: 10.1007/s13324-019-00317-7
Abstract: We study non-regularity of growth of the fractional Cauchy transform $$\begin{aligned} f(z)=\int _{-\pi }^{\pi } \frac{d\psi (t)}{(1-ze^{-it})^\alpha }, \quad \alpha >0, \psi \in BV[-\pi ,\pi ], \end{aligned}$$f(z)=∫-ππdψ(t)(1-ze-it)α,α>0,ψ∈BV[-π,π],in terms of the modulus of continuity of the… read more here.
Keywords: asymptotic behavior; fractional cauchy; cauchy transform; behavior fractional ... See more keywords
The Cauchy transform in the slice hyperholomorphic setting and related topics
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2018.12.007
Abstract: Abstract In this paper we study the additive splitting associated to the quaternionic Cauchy transform defined by the Cauchy formula of slice hyperholomorphic functions. Moreover, we introduce and study the analogue of the fundamental solution… read more here.
Keywords: slice; setting related; hyperholomorphic setting; slice hyperholomorphic ... See more keywords
Starlikeness and convexity of Cauchy transform on equilateral triangle
Sign Up to like & getrecommendations! Published in 2019 at "Complex Variables and Elliptic Equations"
DOI: 10.1080/17476933.2019.1671832
Abstract: ABSTRACT Let Δ be an equilateral triangle, we define the Cauchy transform of the normalized two-dimensional Lebesgue measure μ on Δ by . We prove that F is univalent and starlike, but not convex in… read more here.
Keywords: convexity cauchy; cauchy transform; transform equilateral; starlikeness convexity ... See more keywords