Publications
2001
Issue 50

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

50/2001

Embeddings of lattices in L^2([0,1], Z)

Valerii N. Berestovskii and Conrad Plaut

Abstract

We show how to construct the group $L^{2} ([0, 1], Z)$ 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 $L^{2} ([0, 1], Z)$ . Finally we prove a similar embedding theorem for integral and p-rational lattices into the $Z$ -module of all continuous integer-valued functions on the group $Z_{p}$ of p-adic integers.

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Received:: 07.08.01

Published:: 07.08.01

MSC Codes:: 52C07, 11H06

Keywords:: lattice, embedding, hadamard matrices, hilbert space, p-adic integers

Related publications

inJournal

2002 Repository Open Access

Valerii N. Berestovskii and Conrad Plaut

Embedding lattices in $L^{2} ([0, 1] Z)$

In: Journal of geometry, 75 (2002) 1-2, pp. 27-45

BibTex DOI: 10.1007/s00022-002-1619-1

MiS Preprint Repository

Embeddings of lattices in L^2([0,1], Z)

Abstract

Related publications

Embedding lattices in L2([0,1]Z)

Embedding lattices in $L^{2} ([0, 1] Z)$