On Boundary Values of Three-Harmonic Poisson Integral on the Boundary of a Unit Disk
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DOI: 10.1007/s11253-018-1548-2
Abstract: Let C0 be a curve in a disk D = {|z| < 1} tangential to a circle at the point z = 1 and let Cθ be the result of rotation of this curve by… read more here.
Keywords: values three; harmonic poisson; three harmonic; integral boundary ... See more keywords
Ultradistributional boundary values of harmonic functions on the sphere
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DOI: 10.1016/j.jmaa.2017.08.035
Abstract: Abstract We present a theory of ultradistributional boundary values for harmonic functions defined on the Euclidean unit ball. We also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their… read more here.
Keywords: harmonic functions; ultradistributional boundary; boundary values; functions sphere ... See more keywords
The Cauchy integral formula and distributional integration
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DOI: 10.1080/17476933.2018.1557159
Abstract: ABSTRACT We study the Cauchy representation formula for analytic functions on the unit disc whose pointwise boundary value function is distributionally integrable. We prove that the formula holds when the distributional boundary values exist, and… read more here.
Keywords: cauchy integral; integral formula; formula; boundary values ... See more keywords
Schoenflies solutions of conformal boundary values may fail to be Sobolev
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DOI: 10.5186/aasfm.2019.4441
Abstract: We show that there exist planar Jordan domains $\Omega_1$ and $\Omega_2$ with boundaries of Hausdorff dimension $1$ such that any conformal maps $\varphi_1 \colon \mathbb D \to \Omega_1$ and $\varphi_2 \colon \Omega_2 \to \mathbb D… read more here.
Keywords: conformal boundary; boundary values; schoenflies solutions; solutions conformal ... See more keywords