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.

Yukawa potentials in the 3-dimensional space.

Representation in Fourier space

The Bessel potential acts by multiplication on the Fourier transforms

Integral representations

can be represented by

by the integral formula

denotes the Gamma function by

This last expression can be more succinctly written in terms of a modified Bessel function, for which the potential gets its name:

Asymptotics

,

the Bessel potential behaves asymptotically as the Riesz potential.

,

See also

• Riesz potential

• Fractional integration

• Sobolev space

• Fractional Schrödinger equation

• Yukawa potential

References