De Branges spaces and local description of submodules of entire functions

We present a scheme of using de Branges spaces theory to study the local description problem for submodules in different spaces of entire functions. Among other things this scheme includes the development of ideas from the paper by Anton Baranov and Yurii Belov (2019). They used de Branges theory as the toolbox for exploring, although in other terms, some unsolved questions on submodules of entire functions which are Fourier-Laplace transforms of compactly supported distributions.