For a certain class of infinite-dimensional vectors of a Hilbert space, we have found a second-degree relation between the elements of a Gramian matrix in the form of equalities and inequalities. For an ordered system of nonorthogonal periodic vector functions, we have determined the Gramian matrices whose nondiagonal elements are connected with the elements of the first column by equalities of degree not higher than 2.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 53, No. 4, pp. 188–197, October–December, 2010.
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Plakhtienko, M.P. Nonclassical relations between elements of Gramian matrices of vector systems of a unitary Hilbert space. J Math Sci 181, 529–540 (2012). https://doi.org/10.1007/s10958-012-0704-8
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DOI: https://doi.org/10.1007/s10958-012-0704-8