Abstract
AbstractLet $$\varOmega $$
Ω
be an open subset of $$\mathbb {R}^{2}$$
R
2
and E a complete complex locally convex Hausdorff space. The purpose of this paper is to find conditions on certain weighted Fréchet spaces $$\mathcal {EV}(\varOmega )$$
EV
(
Ω
)
of smooth functions and on the space E to ensure that the vector-valued Cauchy–Riemann operator $${\overline{\partial }}:\mathcal {EV}(\varOmega ,E)\rightarrow \mathcal {EV}(\varOmega ,E)$$
∂
¯
:
EV
(
Ω
,
E
)
→
EV
(
Ω
,
E
)
is surjective. This is done via splitting theory and positive results can be interpreted as parameter dependence of solutions of the Cauchy–Riemann operator.
Funder
Technische Universität Hamburg
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
Reference67 articles.
1. Agranovich, M.S.: Partial differential equations with constant coefficients. Rus. Math. Surv. 16(2), 23 (1961). https://doi.org/10.1070/rm1961v016n02abeh004104
2. Bierstedt, K.D., Pietsch, A., Ruess, W.M., Vogt, D. (eds.): Functional Analysis (Proc., Essen, 1991), Lect. Notes in Pure and Appl. Math. 150. Dekker, New York (1994)
3. Bonet, J., Domański, P.: Parameter dependence of solutions of partial differential equations in spaces of real analytic functions. Proc. Am. Math. Soc. 129(2), 495–503 (2001). https://doi.org/10.1090/S0002-9939-00-05867-6
4. Bonet, J., Domański, P.: Parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences. J. Funct. Anal. 230(2), 329–381 (2006). https://doi.org/10.1016/j.jfa.2005.06.007
5. Bonet, J., Domański, P.: The structure of spaces of quasianalytic functions of Roumieu type. Arch. Math. (Basel) 89(5), 430–441 (2007). https://doi.org/10.1007/s00013-007-2073-y
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