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- W4361003022 abstract "Abstract In this paper we consider the classical $${overline{partial }}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mover> <mml:mi>∂</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> -problem in the case of one complex variable both for analytic and polyanalytic data. We apply the decomposition property of polyanalytic functions in order to construct particular solutions of this problem and obtain new Hörmander type estimates using suitable powers of the Cauchy-Riemann operator. We also compute particular solutions of the $${overline{partial }}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mover> <mml:mi>∂</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> -problem for specific polyanalytic data such as the Itô complex Hermite polynomials and polyanalytic Fock kernels." @default.
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- W4361003022 date "2023-03-27" @default.
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- W4361003022 title "Hörmander’s $$L^2$$-Method, $${overline{partial }}$$-Problem and Polyanalytic Function Theory in One Complex Variable" @default.
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- W4361003022 doi "https://doi.org/10.1007/s11785-023-01340-0" @default.
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