In Hodge theory, the anticommutator of the exterior derivative and its adjoint operator gives the operator named for this method's namesake; functions in the null space of that operator are said to be harmonic.
It is effectively unique, according to Lerch's Theorem. It can be inverted numerically using Talbot's method or Weeks' method or analytically using a vertical contour in a Bromwich integral, and in some cases the inverse can be obtained using Duhamel's Convolution Principle. In Hodge theory, the anticommutator of the exterior derivative and its adjoint operator gives the operator named for this method's namesake; functions in the null space of that operator are said to be harmonic. This method has largely replaced Heaviside's operational calculus as a technique for turning differential equations into algebraic equations. FTP, name this integral transform which reduces to the Fourier transform when s equals i omega.
It is effectively unique, according to Lerch's Theorem. It can be inverted numerically using Talbot's method or Weeks' method or analytically using a vertical contour in a Bromwich integral, and in some cases the inverse can be obtained using Duhamel's Convolution Principle.
{Laplace transform}