The kelvin transform

Potential Theory ◽

10.1007/978-3-662-12727-8_12 ◽

1974 ◽

pp. 84-90

Author(s):

John Wermer

Keyword(s):

Kelvin Transform

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Kelvin transform for α-harmonic functions in regular domains

Demonstratio Mathematica ◽

10.1515/dema-2013-0370 ◽

2012 ◽

Vol 45 (2) ◽

Author(s):

Krzysztof Michalik ◽

Michał Ryznar

Keyword(s):

Lipschitz Domain ◽

Harmonic Functions ◽

Stable Processes ◽

Kelvin Transform

AbstractWe investigate conditional stable processes in a Lipschitz domain

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Space and time inversions of stochastic processes and Kelvin transform

Mathematische Nachrichten ◽

10.1002/mana.201700152 ◽

2018 ◽

Vol 292 (2) ◽

pp. 252-272

Author(s):

L. Alili ◽

L. Chaumont ◽

P. Graczyk ◽

T. Żak

Keyword(s):

Stochastic Processes ◽

Kelvin Transform ◽

Space And Time

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On Radon transforms between lines and hyperplanes

International Journal of Mathematics ◽

10.1142/s0129167x17500938 ◽

2017 ◽

Vol 28 (13) ◽

pp. 1750093 ◽

Cited By ~ 3

Author(s):

Boris Rubin ◽

Yingzhan Wang

Keyword(s):

Radon Transform ◽

Symmetric Case ◽

Fractional Integrals ◽

Radon Transforms ◽

Full Generality ◽

Inversion Formulas ◽

Radial Functions ◽

Kelvin Transform ◽

Funk Transform ◽

Dual Transform

We obtain new inversion formulas for the Radon transform and its dual between lines and hyperplanes in [Formula: see text]. The Radon transform in this setting is non-injective and the consideration is restricted to the so-called quasi-radial functions that are constant on symmetric clusters of lines. For the corresponding dual transform, which is injective, explicit inversion formulas are obtained both in the symmetric case and in full generality. The main tools are the Funk transform on the sphere, the Radon-John [Formula: see text]-plane transform in [Formula: see text], the Grassmannian modification of the Kelvin transform, and the Erdélyi–Kober fractional integrals.

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