Global solvability on two-step compact nilmanifolds
Global solvability on two-step compact nilmanifolds
We apply the methods of representation theory of nilpotent Lie groups to study the convergence of Fourier series of smooth global solutions to first order invariant partial differential equations <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D f equals g"> <mml:semantics> <mml:mrow> <mml:mi>D</mml:mi> <mml:mi>f</mml:mi> <mml:mo>=</mml:mo> <mml:mi>g</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">Df = g</mml:annotation> </mml:semantics> …