caa a22 4500 475741218 CHVBK 20180406123500.0 cr unu---uuuuu 170329e20000801xx s 000 0 eng 10.1007/BF02675339 doi (NATIONALLICENCE)springer-10.1007/BF02675339 The Levin-Golovin theorem for sobolev spaces [Elektronische Daten] [S. Avdonin, S. Ivanov] We obtain sufficient conditions for the basis property of the family of exponentials $$\{ e^{i\lambda _n t} /(1 + |\lambda _n |^s )\} _{n \in \mathbb{Z}} $$ in the Sobolev spaceH s (0,a) in terms of the behavior of the generating function, which is an entire function of exponential type with zeros λ n . This result is a generalization of the Levin-Golovin theorem on the basis property of the family of exponentials generated by a function of sine type inL 2(0,a). We apply the theorem obtained to the interpolation of entire functions of exponential type; this application is a generalization of the Kotel'nikov-Shannon theorem in signal theory. Kluwer Academic/Plenum Publishers, 2000 family of exponential functions nationallicence basis property nationallicence Levin-Golovin theorem nationallicence interpolation of entire functions nationallicence signal theory nationallicence Avdonin S. Saint-Petersburg State University, Saint-Petersburg, USSR aut Ivanov S. Saint-Petersburg State University, Saint-Petersburg, USSR aut Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/2(2000-08-01), 145-153 0001-4346 68:2<145 2000 68 11006 https://doi.org/10.1007/BF02675339 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02675339 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Avdonin S. Saint-Petersburg State University, Saint-Petersburg, USSR aut NATIONALLICENCE 700 1- Ivanov S. Saint-Petersburg State University, Saint-Petersburg, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/2(2000-08-01), 145-153 0001-4346 68:2<145 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer