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- W4290041808 abstract "It has been shown that for several nilpotent Gelfand pairs (N,K) (i.e., with N a nilpotent Lie group, K a compact group of automorphisms of N and the algebra L^1(N)^K commutative) the spherical transform establishes a 1-to-1 correspondence between the space S(N)^K of K-invariant Schwartz functions on N and the space S({Sigma}) of functions on the Gelfand spectrum {Sigma} of L^1(N)^K which extend to Schwartz functions on Rd, once {Sigma} is suitably embedded in Rd. We call this property (S). We present here a general bootstrapping method which allows to establish property (S) to new nilpotent pairs (N,K), once the same property is known for a class of quotient pairs of (N,K) and a K-invariant form of Hadamard formula holds on N. We finally show how our method can be recursively applied to prove property (S) for a significant class of nilpotent Gelfand pairs." @default.
- W4290041808 created "2022-08-06" @default.
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- W4290041808 date "2017-06-05" @default.
- W4290041808 modified "2023-10-16" @default.
- W4290041808 title "Nilpotent gelfand pairs and Schwartz extensions of spherical transforms via quotient pairs" @default.
- W4290041808 doi "https://doi.org/10.48550/arxiv.1706.01390" @default.
- W4290041808 hasPublicationYear "2017" @default.
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