Mathematics, Artificial Intelligence, Machine Learning, Deep Learning, AI.
typically large, dense, and computationally intensive to handle. The Spectral Decomposition of the Fractional Laplacian For a function u defined in an appropriate Sobolev space, the fractional Laplacian can be described spectrally in 𝑅𝑑 as follows: where ⟨⋅,⋅⟩ denotes the inner product in L2(Rd).