Preprint 50/2001

Embeddings of lattices in L2([0,1], Z)

Valerii N. Berestovskii and Conrad Plaut

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Submission date: 07. Aug. 2001
Pages: 19
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 tex2html_wrap_inline69 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 tex2html_wrap_inline69. Finally we prove a similar embedding theorem for integral and p-rational lattices into the tex2html_wrap_inline81-module of all continuous integer-valued functions on the group tex2html_wrap_inline83 of p-adic integers.

03.04.2017, 12:08