De Branges's theorem

De Branges's theorem, often referred to in the context of de Branges spaces, is a significant result in the theory of entire functions, specifically related to the representation of certain types of entire functions through Hilbert spaces. The theorem addresses the existence of entire functions that can be represented in terms of their zeros and certain properties related to their growth and behavior. More formally, it provides conditions under which a function defined by its Taylor series can be expressed in terms of its zeros or certain integral representations.