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My question concerns the name for determinants of Hankel-matrices $H = (s_{i+j})_{i,j = 0}^n$.

In the classical textbook of Shohat and Tamarkin (1943) "The Problem of Moments", these determinants are defined without a name (on page viii).

In several math articles, I found the name Hankel determinant. In the field of physics (especially methods of moments), where I work, however, the common name seems to be "Hankel-Hadamard determinant"

Does anyone can give me a hint on how Hadamard is connected to this? Any help would be highly appreciated!

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Some background is given in the appendix of this 1988 paper by Handy and Bessis, who apparently introduced this terminology: Hankel-Hadamard matrix, Hankel-Hadamard determinant, Hankel-Hadamard positivity, Hankel-Hadamard inequality. It refers to a class of matrices of the Hankel form (constant diagonals) with a determinant that satisfies a generalized Hadamard inequality. The inequality is not quite the original Hadamard inequality (it's a lower bound rather than an upper bound on the determinant), but the name stuck.

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  • $\begingroup$ @Carlo Thank you very much indeed! I stumbled across the Handy and Bessis (1988) paper quite frequently when looking for an answer myself. As my institute does not subscribe to the APS "Physical Review A" Journal, however, I could not see the contents. Now I will try to get hold of a copy via interlibrary loan. Thanks again!! $\endgroup$ – Maria Z Jun 20 '13 at 6:51

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