Results 11 to 20 of about 11,431,351 (352)
Harmonic functions with varying coefficients
Journal of Inequalities and Applications, 2016 Complex-valued harmonic functions that are univalent and sense preserving in the open unit disk can be written in the form f = h + g ‾ $f=h+\overline{g}$ , where h and g are analytic.
Jacek Dziok +2 more
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Explorations in Complex Functions, 2020 Richard Beals, Roderick S. C. Wong
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Axially Harmonic Functions and the Harmonic Functional Calculus on the S-spectrum [PDF]
Journal of Geometric Analysis, 2022 The spectral theory on the S-spectrum was introduced to give an appropriate mathematical setting to quaternionic quantum mechanics, but it was soon realized that there were different applications of this theory, for example, to fractional heat diffusion ...
F. Colombo +3 more
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A series expansion for generalized harmonic functions
Analysis and Mathematical Physics, 2021 We consider a class of generalized harmonic functions in the open unit disc in the complex plane. Our main results concern a canonical series expansion for such functions. Of particular interest is a certain individual generalized harmonic function which
Markus Klintborg, A. Olofsson
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Deformations Of Multivalued Harmonic Functions [PDF]
Quarterly Journal of Mathematics, 2019 We consider harmonic sections of a bundle over the complement of a codimension 2 submanifold in a Riemannian manifold, which can be thought of as multivalued harmonic functions.
S. Donaldson
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Harmonic Functions, Conjugate Harmonic Functions and the Hardy Space $$H^1$$H1 in the Rational Dunkl Setting [PDF]
Journal of Fourier Analysis and Applications, 2018 In this work we extend the theory of the classical Hardy space $$H^1$$H1 to the rational Dunkl setting. Specifically, let $$\Delta $$Δ be the Dunkl Laplacian on a Euclidean space $$\mathbb {R}^N$$RN. On the half-space $$\mathbb {R}_+\times \mathbb {R}^N$$
Jean-Philippe Anker +2 more
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Harmonic functions on mated-CRT maps [PDF]
Electronic Journal of Probability, 2018 A mated-CRT map is a random planar map obtained as a discretized mating of correlated continuum random trees. Mated-CRT maps provide a coarse-grained approximation of many other natural random planar map models (e.g., uniform triangulations and spanning ...
Ewain Gwynne, Jason Miller, S. Sheffield
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On s-harmonic functions on cones. [PDF]
, 2017 We deal with non negative functions satisfying \[ \left\{ \begin{array}{ll} (-\Delta)^s u_s=0 & \mathrm{in}\quad C, u_s=0 & \mathrm{in}\quad \mathbb{R}^n\setminus C, \end{array}\right.
S. Terracini, Giorgio Tortone, S. Vita
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Uniform rectifiability from Carleson measure estimates and ε-approximability of bounded harmonic functions [PDF]
Duke mathematical journal, 2016 Let $\Omega\subset\mathbb R^{n+1}$, $n\geq1$, be a corkscrew domain with Ahlfors-David regular boundary. In this paper we prove that $\partial\Omega$ is uniformly $n$-rectifiable if every bounded harmonic function on $\Omega$ is $\varepsilon ...
J. Garnett, Mihalis Mourgoglou, X. Tolsa
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Multiply Harmonic Functions [PDF]
Nagoya Mathematical Journal, 1966 Let Ω and Ω′ be two locally compact, connected Hausdorff spaces having countable bases. On each of the spaces is defined a system of harmonic functions satisfying the axioms of M. Brelot [2]. The following is the description of such a system. To each open set of Ω is assigned a vector space of finite continuous functions, called the harmonic functions,
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