caa a22 4500 46319618X CHVBK 20180406164923.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s10773-007-9418-y doi (NATIONALLICENCE)springer-10.1007/s10773-007-9418-y Convolution of Ultradistributions, Field Theory, Lorentz Invariance and Resonances [Elektronische Daten] [C. Bollini, P. Marchiano, M. Rocca] In this work, a general definition of convolution between two arbitrary Ultradistributions of Exponential type (UET) is given. The product of two arbitrary UET is defined via the convolution of its corresponding Fourier Transforms. Some examples of convolution of two UET are given. Expressions for the Fourier Transform of spherically symmetric (in Euclidean space) and Lorentz invariant (in Minkowskian space) UET in term of modified Bessel distributions are obtained (Generalization of Bochner's theorem). The generalization to UET of dimensional regularization in configuration space is obtained in both, Euclidean and Minkowskian spaces As an application of our formalism, we give a solution to the question of normalization of resonances in Quantum Mechanics. General formulae for convolution of even, spherically symmetric and Lorentz invariant UET are obtained and several examples of application are given. Springer Science+Business Media, LLC, 2007 Bollini C. Departamento de Física, Fac. de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, (1900), La Plata, Argentina aut Marchiano P. Departamento de Física, Fac. de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, (1900), La Plata, Argentina aut Rocca M. Departamento de Física, Fac. de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, (1900), La Plata, Argentina aut International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/12(2007-12-01), 3030-3059 0020-7748 46:12<3030 2007 46 10773 https://doi.org/10.1007/s10773-007-9418-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-007-9418-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bollini C. Departamento de Física, Fac. de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, (1900), La Plata, Argentina aut NATIONALLICENCE 700 1- Marchiano P. Departamento de Física, Fac. de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, (1900), La Plata, Argentina aut NATIONALLICENCE 700 1- Rocca M. Departamento de Física, Fac. de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, (1900), La Plata, Argentina aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/12(2007-12-01), 3030-3059 0020-7748 46:12<3030 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer