Embeddings of lattices in L2([0,1], Z)
Valerii N. Berestovskii and Conrad Plaut
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Submission date: 07. Aug. 2001
published in: Journal of geometry, 75 (2002) 1-2, p. 27-45
with the following different title: Embedding lattices in L2 ([0,1],Z)
MSC-Numbers: 52C07, 11H06
Keywords and phrases: lattice, embedding, hadamard matrices, hilbert space, p-adic integers
We show how to construct the group using any sequence of Hadamard matrices. This construction is nicely compatible with the classical Haar and Rademacher functions. We then show that every k-dimensional Euclidean lattice is isometrically isomorphic to a k-slice of . Finally we prove a similar embedding theorem for integral and p-rational lattices into the -module of all continuous integer-valued functions on the group of p-adic integers.