Reconstruction of eigenfunctions of a q-ary n-dimensional hypercube

Reconstruction of eigenfunctions of a q-ary n-dimensional hypercube We prove that values of an arbitrary eigenfunction of a q-ary n-dimensional hypercube can be uniquely reconstructed at all vertices inside a ball if its values on the corresponding sphere are known; we give sufficient conditions for such reconstruction in terms of the eigenvalue and the ball radius. We show that in the case where values of an eigenfunction are given on a sphere of radius equal to the corresponding eigenvalue, all values of the eigenfunction can be reconstructed; similarly to the previous case, sufficient numerical conditions are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Reconstruction of eigenfunctions of a q-ary n-dimensional hypercube

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Publisher
Pleiades Publishing
Copyright
Copyright © 2015 by Pleiades Publishing, Inc.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946015030035
Publisher site
See Article on Publisher Site

Abstract

We prove that values of an arbitrary eigenfunction of a q-ary n-dimensional hypercube can be uniquely reconstructed at all vertices inside a ball if its values on the corresponding sphere are known; we give sufficient conditions for such reconstruction in terms of the eigenvalue and the ball radius. We show that in the case where values of an eigenfunction are given on a sphere of radius equal to the corresponding eigenvalue, all values of the eigenfunction can be reconstructed; similarly to the previous case, sufficient numerical conditions are presented.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 18, 2015

References

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