 Later, he worked in the theory of partial differential equations, where he introduced the "Carleman estimates", and found a way to study the spectral asymptotics of Schrödinger operators.In 1932, following the work of Henri Poincaré, Erik Ivar Fredholm, and Bernard Koopman, he devised the "Carleman embedding" (also called "Carleman linearization"), a way to embed a finite-dimensional system of nonlinear differential equations  = P(u) for u