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Sibirsk. Mat. Zh., 2017, Volume 58, Number 1, Pages 185–198 (Mi smj2851)  

This article is cited in 1 scientific paper (total in 1 paper)

Solvability of the inhomogeneous Cauchy–Riemann equation in projective weighted spaces

D. A. Polyakovaab

a Southern Federal University, Faculty of Mathematics, Mechanics and Computer Sciences, Rostov-on-Don, Russia
b Southern Mathematical Institute, Vladikavkaz, Russia

Abstract: We establish an analog of Hörmander's Theorem on solvability of the inhomogeneous Cauchy–Riemann equation for a space of measurable functions satisfying a system of uniform estimates. The result is formulated in terms of the weight sequence defining the space. The same conditions guarantee the weak reducibility of the corresponding space of entire functions. Basing on these results, we solve the problem of describing the multipliers in weighted spaces of entire functions with the projective and inductive-projective topological structure. Applications are obtained to convolution operators in the spaces of ultradifferentiable functions of Roumieu type.

Keywords: inhomogeneous Cauchy–Riemann equation, projective weighted space, multiplier, convolution operator.

DOI: https://doi.org/10.17377/smzh.2017.58.118

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English version:
Siberian Mathematical Journal, 2017, 58:1, 142–152

Bibliographic databases:

UDC: 517.982
MSC: 35R30
Received: 19.02.2016

Citation: D. A. Polyakova, “Solvability of the inhomogeneous Cauchy–Riemann equation in projective weighted spaces”, Sibirsk. Mat. Zh., 58:1 (2017), 185–198; Siberian Math. J., 58:1 (2017), 142–152

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. V. Abanin, T. M. Andreeva, “O syur'ektivnosti operatora svertki v prostranstvakh golomorfnykh v oblasti funktsii zadannogo rosta”, Vladikavk. matem. zhurn., 20:2 (2018), 3–15  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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