Global solvability for a class of variable-coefficient Vekua-type operators on compact lie groups

We investigate the global solvability of a class of Vekua-type operators in the form: aligned Pu = Lu - (s(t) + iδ q(t)) · u - α q(t) ū, aligned P u = L u - ( s ( t ) + i δ q ( t ) ) · u - α q ( t ) u ¯ , which act on smooth functions defined on T¹ × G T 1 × G , where G G is a compact Lie group. The operator L L is given by aligned L = ∂ ₜ - (p₀ + iλ q(t)) · D, aligned L = ∂ t - ( p 0 + i λ q ( t ) ) · D , with D D being a diagonal operator on G G . The term ū u ¯ makes P P real-linear but not complex-linear, leading to significant differences in the analysis of global solvability. We establish that P P is globally solvable in a smooth sense under specific non-resonance assumptions.