2006/05/31 by C. G. Bollini, P. Marchiano, Pilar Marchiano +1 · 44 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Classical mechanics #Convolution (computer science) #Convolution theorem #Euclidean space #Fourier analysis #Fourier transform #Fractional Fourier transform #Lorentz covariance #Lorentz transformation #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Physics #Pure mathematics #Quantum Mechanics and Applications #hep-th
paper · pdf · doi:10.1007/s10773-007-9418-y
published in International Journal of Theoretical Physics 46(12), 3030-3059 (Springer Science+Business Media) · 56 pages. Accepted for publication in International Journal of Theoretical Physics on June 19, 2006
arxiv created 2007/04/24 · openalex publication_date 2007/08/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.