### Unitary extensions of isometries, generalized interpolation and band extensions

The aim of this paper is to give a very brief account of some applications of the method of unitary extensions of isometries to interpolation and extension problems.

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The aim of this paper is to give a very brief account of some applications of the method of unitary extensions of isometries to interpolation and extension problems.

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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