Тензорные поля на плоскости и преобразования Рисса Full article
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Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2014, Volume: 11, Pages: 709–724 Pages count : | ||
| Tags | solenoidal, potential tensor fields, Helmholtz decomposition, singular integral operators, Riesz transforms, Beltrami systems. | ||
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Abstract:
In this paper we study symmetric tensor fields via complex coordinate system. The formulas for divergence δ and symmetric gradient d of tensor fields in complex variables are derived thus we get the equations of Beltrami type. We obtain the general representation for the solenoidal tensor fields on the plane, which involves the Riesz transforms, their powers and the one real generating function f∈L2(R2). We present also the Helmholtz decomposition of the tensor fields in terms of Riesz transforms.
Cite:
Казанцев С.Г.
Тензорные поля на плоскости и преобразования Рисса
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2014. Т.11. С.709–724.
Тензорные поля на плоскости и преобразования Рисса
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2014. Т.11. С.709–724.
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