TL;DR
This paper characterizes interpolating sequences of matrix tuples in both commuting and non-commuting cases using reproducing kernel Hilbert spaces and analytic functions, providing theoretical insights and examples.
Contribution
It offers a new characterization of interpolating sequences of matrix tuples in both commuting and non-commuting cases, using separation conditions and analytic functions.
Findings
Characterization of interpolating sequences via reproducing kernel Hilbert spaces
Sufficient conditions for interpolation using analytic functions
Examples illustrating the theoretical results
Abstract
We study interpolating sequences of -tuples of matrices, by looking at the commuting and the non-commuting case separately. In both cases, we will give a characterization of such sequences in terms of separation conditions on suitable reproducing kernel Hilbert spaces, and we will give sufficient conditions stated in terms of separation via analytic functions. Examples of such interpolating sequences will also be given
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Topics in Algebra · Approximation Theory and Sequence Spaces