Unverified50% confidenceFactExact time
The Sobolev space H^s can be equivalently described as the space of functions whose Peter–Weyl expansion coefficients remain square-integrable after being weighted by the s-th power of the eigenvalues; the larger s is, the smoother the function and the faster the high-frequency coefficients decay.
1
Sources
50%
Confidence
Long-term
Relevance
10/12/2026
First Seen
Sources
Related Entities
Related Claims
UnverifiedThe Peter–Weyl theorem decomposes the space L^2(G) of square-integrable functions on a compact group into an orthogonal direct sum of subspaces spanned by the matrix coefficients of all irreducible unitary representations, with each irreducible representation appearing with a multiplicity equal to its dimension.78% similarUnverifiedThe squared exponential kernel corresponds to the class of infinitely smooth functions, while the Matérn-ν kernel corresponds to the class of ν-times differentiable functions, with smaller ν yielding rougher function classes.70% similarUnverified一维Wasserstein-1距离等于两个累积分布函数之间面积的积分 W₁ = ∫|F_A(x) - F_B(x)|dx68% similarUnverifiedSpherical harmonics characterize angular momentum by order l, where l=0 corresponds to scalars, l=1 corresponds to vectors, and higher orders correspond to tensor representations.63% similarVerifiedThe mathematical definition of the ReLU activation function is f(x) = max(0, x), which can effectively mitigate the vanishing gradient problem compared to Sigmoid and Tanh.63% similar
Cite This Claim
Stable URI
https://kongchang.com/claim/1001363API
curl https://kongchang.com/api/v1/knowledge/claims/1001363MCP
get_claim(id=1001363)