Parole chiave

• shift-invariant space
• discrete analytic function
• rhombic lattice
• Schur function

Abstract There are several known generalizations of the Beurling-Lax theorem that establish a correspondence between shift-invariant spaces of analytic functions and Schur functions. The situation becomes more complicated when the usual notion of analyticity is replaced with a discrete analogue due to J. Ferrand and R. J. Duffin. It turns out that for a suitably defined shift operator, one can still describe shift-invariant reproducing kernel Hilbert spaces of discrete analytic functions on a rhombic lattice in terms of the convolution product and discrete analytic Schur functions.

This is joint work with D. Alpay and A. Fuerte Perez.