Every convolution-invertible complex measure on R^n is a convolution of a translation, finitely many orthogonal embeddings of a fixed one-dimensional measure σ, and an exponential exp(ν).
Berger, On quasi-infinitely divisible distributions with a point mass
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Invertible Complex Measures on Euclidean Spaces
Every convolution-invertible complex measure on R^n is a convolution of a translation, finitely many orthogonal embeddings of a fixed one-dimensional measure σ, and an exponential exp(ν).