An Introduction to Heisenberg Groups
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چکیده
for all x, x ∈ R. Also, Tx is the identity operator only when x = 0, and thus the correspondence x 7→ Tx provides an isomorphic embedding of R , as an abelian group, into the group of invertible linear operators on the vector space of continuous functions with compact support on R under the binary operation composition. Of course there are numerous other vector spaces of functions on R that one might use here. For each y in R define a linear operator Uy on the same space of functions on R by Uy(f)(w) = exp(2πi λ y · w) f(w), (3)
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تاریخ انتشار 2002