Volume 48, Issue 4
Cauchy Matrices in the Observation of Diffusion Equations

J. Math. Study, 48 (2015), pp. 330-344.

Published online: 2015-12

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• Abstract
Observability Gramians of diffusion equations have been recently connected to infinite Pick and Cauchy matrices. In fact, inverse or observability inequalities can be obtained after estimating the extreme eigenvalues of these structured matrices,with respect to the diffusion semi-group matrix. The purpose is hence to conduct a spectral study of a subclass of symmetric Cauchy matrices and present an algebraic way to show the desired observability results. We revisit observability inequalities for three different observation problems of the diffusion equation and show how they can be (re)stated through simple proofs.
• Keywords

Pick matrices Cauchy matrices Hadamard product diffusion equation observability inequalities

• AMS Subject Headings

15B05, 15B34, 93B07, 35K05