Local solvability of the $\overline{\partial}$-equations on $l^{2}$

Kheira Memchout-Abdallah Talhaoui
2020 Proceedings of the Institute of Mathematics and Mechanics,National Academy of Sciences of Azerbaijan  
In this work, we establish sufficient conditions for the existence of solutions of the Cauchy-Riemann equations on the unit ball B of the Hilbert space l 2 for a particular class of ∂-closed C ∞ smooth (0,1)-forms ω. The used method is based on the expansion in Fourier series of the indefinitely differentiable functions on the closed unit ball of ii) The series (1.2) is supposed to be absolutely convergent.
doi:10.29228/proc.18 fatcat:te5lqgd6ejgldj6py3r3gtclua