In mathematics, the Bessel potential is a potential (named after Friedrich Wilhelm Bessel) similar to the Riesz potential but with better decay properties at infinity.
If s is a complex number with positive real part then the Bessel potential of order s is the operator where Δ is the Laplace operator and the fractional power is defined using Fourier transforms.
The Bessel potential acts by multiplication on the Fourier transforms: for each
can be represented by where the Bessel kernel
denotes the Gamma function.
The Bessel kernel can also be represented for
by[2] This last expression can be more succinctly written in terms of a modified Bessel function,[3] for which the potential gets its name: At the origin, one has as
the Bessel potential behaves asymptotically as the Riesz potential.