ABSTRACT
This chapter presents the organisational structure and the layout. It relates the classical Shannon sampling theorem to an Euler-type summation formula. Shannon-type sampling including all manifestions of over- and undersampling for arbitrary lattices Λ⊂R is provided for arbitrary finite reference intervals and the whole Euclidean space R (under certain conditions at infinity for the functions under consideration). The applicability of the results is studied by specifying certain cases of generalized sinc-functions and associated cardinal series expansions.
