Dipartimento di Matematica e Informatica Nell'ambito del programma Visiting Professor 2011/2012, finanziato dalla Regione Autonoma della Sardegna il Prof. Stevan Pilipovic dell'University of Novi Sad, Serbia full member of the Serbian Academy of Sciences VP per 3 mesi presso il Dipartimento di Matematica e Informatica terra'il seguente seminario SEQUENTIAL APPROACH TO FUNCTION SPACES AND EIGENFUNCTION EXPANSIONS Giovedi, 22. 12. 2011, aula D (sede via Ospedale)ore 16.00 Abstract: We outline an approach for characterization of classical functional spaces defined on $R^n$ like the Schwartz space and the Gelfand-Shilov spaces by means of Fourier expansions. We present recent results cocnerned with the definition of such spaces by eigenfunction expansions associated to globally elliptic operators (introduced by Shubin), generalizing the harmonic oscillator case. We present applications for global regularity of the solutions to some degenerate Shubin type PDEs modelled by the so called twisted Laplacian.