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Christoffel–Darboux sources

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Abstract

A new, to the best of our knowledge, class of partially coherent sources is introduced on the basis of the Christoffel–Darboux (CD) formula read as the expression of a possible cross-spectral density. It will be seen that such an interpretation is possible because the CD formula gives the reproducing kernel of a suitable Hilbert space. After discussing general properties of CD kernels, a specific example is worked out using Hermite polynomials. A connection with the density matrix will be highlighted.

© 2021 Optical Society of America

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