caa a22 4500 465810799 CHVBK 20180323112115.0 cr unu---uuuuu 170327e19901101xx s 000 0 eng 10.1007/BF02820305 doi (NATIONALLICENCE)springer-10.1007/BF02820305 Cesàro summability of the Fourier integral representations of the Bloch-Nordsieck distribution and its derivatives [Elektronische Daten] [C. Basili, E. Etim, M. Pallotta] Summary: The Fourier integral representations for the Bloch-Nordsieck distribution ρ(ω) and its derivatives ϱ(n)(ω)(n=1,2,...) are not Cauchy convergent. The theory therefore contains ambiguities. Consequently the equations, characterising the theory and which relate these derivatives to the discrete translations ρ(ω−mE)(m=0, 1, 2, ...,n) of ρ(ω) are not satisfied by these representations as they stand. The equations are consistently satisfied only by the regularised forms of the corresponding integrals. This regularization is carried out in this paper using the method of Cesàro summability. This allows to compute these derivatives ϱ(n)(ω)(n=0,1,2,...) and to investigate their behaviour as functions of ω in the entire half-line 0≤ω<∞. Società Italiana di Fisica, 1990 PACS 12.90 - Miscellaneous theoretical ideals and models nationallicence Basili C. Laboratori Nazionali Frascati, INFN, Frascati, Roma aut Etim E. Laboratori Nazionali Frascati, INFN, Frascati, Roma aut Pallotta M. Laboratori Nazionali Frascati, INFN, Frascati, Roma aut Il Nuovo Cimento A (1965-1970) Società Italiana di Fisica 103/11(1990-11-01), 1595-1606 103:11<1595 1990 103 40763 https://doi.org/10.1007/BF02820305 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02820305 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Basili C. Laboratori Nazionali Frascati, INFN, Frascati, Roma aut NATIONALLICENCE 700 1- Etim E. Laboratori Nazionali Frascati, INFN, Frascati, Roma aut NATIONALLICENCE 700 1- Pallotta M. Laboratori Nazionali Frascati, INFN, Frascati, Roma aut NATIONALLICENCE 773 0- Il Nuovo Cimento A (1965-1970) Società Italiana di Fisica 103/11(1990-11-01), 1595-1606 103:11<1595 1990 103 40763 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer