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Harmonic spirallike functions and harmonic strongly starlike functions

open access: yesMonatshefte Fur Mathematik, 2022
Harmonic functions are natural generalizations of conformal mappings. In recent years, a lot of work have been done by some researchers who focus on harmonic starlike functions. In this paper, we aim to introduce two classes of harmonic univalent functions of the unit disk, called hereditarily $λ$-spirallike functions and hereditarily strongly starlike
Toshiyuki Sugawa   +2 more
exaly   +3 more sources
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Spaces of Harmonic Functions

Journal of the London Mathematical Society, 2000
The paper is mainly concerned with the dimensions of certain spaces of harmonic functions on a complete Riemannian manifold \(M\) of dimension \(n\). It is shown that the study of harmonic functions on \(M\) can be reduced to the study of harmonic functions on each end of \(M\).
Sung, Chiung-Jue   +2 more
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Harmonic Functions on Manifolds

The Annals of Mathematics, 1997
For an open manifold \(M^n\), given a point \(p\in M^n\), let \(r\) be the distance from \(p\). Define \({\mathcal H}_d(M^n)\) to be the linear space of harmonic functions with order of growth at most \(d\). The main result of this paper is a proof of the following Yau's conjecture: Conjecture. For an open manifold with nonnegative Ricci curvature, the
Colding, Tobias H.   +1 more
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Sets of Harmonicity for Finely Harmonic Functions

Potential Analysis, 2004
The author establishes the sharpness of a theorem of Fuglede. \textit{B. Fuglede} [Ann. Inst. Fourier 24, No. 4, 77--91 (1974; Zbl 0287.31003)] observed the following result. Let \(U\) be an open set in \({\mathbb R}^n\) (\(n\geq 2\)). If \(u\) is finely harmonic on \(U\), then there is a dense open subset \(V\) of \(U\) on which \(u\) is harmonic. The
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A Threshold Function for Harmonic Update

SIAM Journal on Discrete Mathematics, 1997
Summary: Harmonic update is a randomized on-line algorithm which, given a random \(m\)-set of vertices \(U(m)\subseteq\{-1,1\}^n\) in the \(n\)-dimensional cube, generates a random vertex \(\mathbf w\in\{-1,1\}^n\) as a putative solution to the system of linear inequalities: \(\sum_{i=1}^n w_i u_i\geq 0\) for each \(\mathbf u\in U(m)\).
Shao C. Fang, Santosh S. Venkatesh
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