The electromagnetic scattering of a spin-0 charged particle off a fixed center is calculated in first-order quantum perturbation theory. This implies evaluating the square of a ‘Dirac delta-function,’ an operation that is not defined in Schwartz distribution theory, and which in elementary text-books is dealt with according to ‘Fermi’s golden rule.’ In this paper these conventional calculations...

Some estimates are proved for the generalized Fourier-Bessel transform in the space (L^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

We elucidate the relation between the two ways of formulating causality in nonlocal quantum field theory: using analytic test functions belonging to the space S (which is the Fourier transform of the Schwartz space D) and using test functions in the Gelfand-Shilov spaces S α. We prove that every functional defined on S 0 has the same carrier cones as its restrictions to the smaller spaces S α. ...

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.

In distribution theory the pullback of a general distribution by a C∞function is well-defined whenever the normal bundle of the C∞-function does not intersect the wavefront set of the distribution. However, the Colombeau theory of generalized functions allows for a pullback by an arbitrary c-bounded generalized function. It has been shown in previous work that in the case of multiplication of C...

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.