Kernels of the so-called a-scale space have the undesirable property of having no closed-form representation in the spatial domain, despite their simple closed-form expression in the Fourier domain. This obstructs spatial convolution or recursive implementation. For this reason an approximation of the 2D a-kernel in the spatial domain is presented using the well-known Gaussian kernel and the Poisson kernel. Experiments show good results, with maximum relative errors of less than 2.4%. The approximation has been successfully implemented in a program for visualizing a-scale spaces. Some examples of practical applications with scale space feature points using the proposed approximation are given.