Unverified50% confidenceFactExact time
The 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.
1
Sources
50%
Confidence
Long-term
Relevance
10/12/2026
First Seen
Sources
Related Entities
Related Claims
UnverifiedThe 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.78% similarUnverified对于SO(3)群，所有不可约表示由非负整数l标记，每个l对应一个(2l+1)维的表示空间，球谐函数Y_l^m是这些表示空间的基向量71% similarUnverified龙曲线的豪斯多夫维度为 2，意味着在无穷迭代极限下能完全填充二维平面区域70% 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火腿三明治定理断言：在n维空间中，对于任意n个可测的物体，总存在一个(n-1)维的超平面能同时将它们逐一二等分69% similar
Cite This Claim
Stable URI
https://kongchang.com/claim/1001361API
curl https://kongchang.com/api/v1/knowledge/claims/1001361MCP
get_claim(id=1001361)