caa a22 4500 465809588 CHVBK 20180323112112.0 cr unu---uuuuu 170327e19900701xx s 000 0 eng 10.1007/BF02782737 doi (NATIONALLICENCE)springer-10.1007/BF02782737 Analytic regularisation of inversion transform integrals by Cesàro summability [Elektronische Daten] [E. Etim, M. Pallotta, C. Basili] Summary: The conformal inversion operator is represented in Hilbert space by Hankel transforms. These transforms occur in a wide variety of problems,e.g. high-energy diffraction scattering, conformal invariant quantum field theory, the improvements of Borel summability of QCD asymptotic expansions, etc. The convergence of these transforms is generally not guaranteed everywhere, hence the need for their regularisation and analytic continuation. It is proposed in this paper that Cesàro summability is not only very simple but also most effective as a method of regularisation and analytic continuation of these integrals. Its power and utility are greatly enhanced by the availability of fast computing facilities. The hierarchy of Cesàro means of the transform integrals is generated, and their convergence investigated, numerically. In all cases we obtain results in agreement with analytic continuation. Cesàro summability can therefore be applied directly to effect the analytic continuation involved in QCD sum rules and not only to the Borel improvements of the relevant integrals. This would provide an additional check of the results obtained via Borel summability. Società Italiana di Fisica, 1990 Other topics in general field and particle theory nationallicence Etim E. INFN, Laboratori Nazionali di Frascati, P.O. Box 13, 00044, Frascati (Roma) aut Pallotta M. INFN, Laboratori Nazionali di Frascati, P.O. Box 13, 00044, Frascati (Roma) aut Basili C. Consiglio Nazionale delle Ricerche, ISRDS, Via Cesare de Lollis 12, 00185, Roma aut Il Nuovo Cimento A (1965-1970) Società Italiana di Fisica 103/7(1990-07-01), 961-982 103:7<961 1990 103 40763 https://doi.org/10.1007/BF02782737 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02782737 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Etim E. INFN, Laboratori Nazionali di Frascati, P.O. Box 13, 00044, Frascati (Roma) aut NATIONALLICENCE 700 1- Pallotta M. INFN, Laboratori Nazionali di Frascati, P.O. Box 13, 00044, Frascati (Roma) aut NATIONALLICENCE 700 1- Basili C. Consiglio Nazionale delle Ricerche, ISRDS, Via Cesare de Lollis 12, 00185, Roma aut NATIONALLICENCE 773 0- Il Nuovo Cimento A (1965-1970) Società Italiana di Fisica 103/7(1990-07-01), 961-982 103:7<961 1990 103 40763 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer