FUNCTIONAL PROPERTIES OF P-DE BRANGES SPACES

This Ph.D. final dissertation studies some analytical properties of the p-de Branges spaces, Hp(E), made up of entire functions and extensively studied in the last thirty years. Besides the first two chapters, where I recall the main properties of the p-de Branges spaces, the rest of the thesis gathers my research work: in the second part, Boundedness of operators, I look for some necessary and sufficient conditions for the boundedness of the translation operators in H2(E) and subsequently for the continuity of the embedding operator ιp,q from Hp(E) into Hq(E). In the third part, Duality results, I characterize the dual of some 1-de Branges spaces. Firstly, I describe the dual of the 1-Bernstein spaces and then I extend the reasonings to some others 1-de Branges spaces.