Riesz potential [SEP] named after
Riesz potential
In mathematics, the Riesz potential is a potential named after its discoverer, the Hungarian mathematician Marcel Riesz. In a sense, the Riesz potential defines an inverse for a power of the Laplace operator on Euclidean space. They generalize to several variables the Riemann–Liouville integrals of one variable.
If 0 < α < "n", then the Riesz potential "I""f" of a locally integrable function "f" on R is the function defined by
where the constant is given
Bessel potential
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 are particular cases of Bessel potentials for formula_2 in the 3-dimensional space.
Representation in Fourier space.
The Bessel potential