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∗ Partially supported by Grant MM-428/94 of MESC.Systems of orthogonal polynomials on the real line play an
important role in the theory of special functions [1]. They find applications
in numerous problems of mathematical physics and classical analysis.
It is known, that classical polynomials have a number of properties, which
uniquely define them.
Several generalized moment problems in two dimensions are particular cases of the general problem of giving conditions that ensure that two isometries, with domains and ranges contained in the same Hilbert space, have commutative unitary extensions to a space that contains the given one. Some results concerning this problem are presented and applied to the extension of functions of positive type.
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