caa a22 4500 475740718 CHVBK 20180406123459.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1023/A:1026644229489 doi (NATIONALLICENCE)springer-10.1023/A:1026644229489 Hilbert Module Realization of the Square of White Noise and Finite Difference Algebras [Elektronische Daten] [L. Accardi, M. Skeide] We develop an approach to the representations theory of the algebra of the square of white noise based on the construction of Hilbert modules. We find the unique Fock representation and show that the representation space is the usual symmetric Fock space. Although we started with one degree of freedom we end up with countably many degrees of freedom. Surprisingly, our representation turns out to have a close relation to Feinsilver's finite difference algebra. In fact, there exists a holomorphic image of the finite difference algebra in the algebra of square of white noise. Our representation restricted to this image is the Boukas representation on the finite difference Fock space. Thus we extend the Boukas representation to a bigger algebra, which is generated by creators, annihilators, and number operators. Plenum Publishing Corporation, 2000 Fock space nationallicence creation nationallicence annihilation and number processes nationallicence white noise nationallicence Feinsilver's finite difference algebra nationallicence Hilbert module nationallicence Boukas representation nationallicence Kolmogorov decomposition nationallicence Accardi L. Center V. Volterra, Università degli Studi di Roma "Tor Vergata”, Italy aut Skeide M. Lehrstuhl für Wahrscheinlichkeitstheorie und Statistik, Brandenburgische Technische Universität Cottbus, Italy aut Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 683-694 0001-4346 68:5-6<683 2000 68 11006 https://doi.org/10.1023/A:1026644229489 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1026644229489 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Accardi L. Center V. Volterra, Università degli Studi di Roma "Tor Vergata”, Italy aut NATIONALLICENCE 700 1- Skeide M. Lehrstuhl für Wahrscheinlichkeitstheorie und Statistik, Brandenburgische Technische Universität Cottbus, Italy aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 683-694 0001-4346 68:5-6<683 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer