On a construction of a frame in the Hardy space defined on the two-dimensional polydisc

In the article we present a construction of a representing system based on the discretized Szego kernel in the Hardy space defined on the two-dimensional polydisc. An answer to the question on the existence of representing systems based on reproducing kernels depends significantly on the space under consideration. It is well known that in the Hardy space there are no both bases and Duffin — Shaeffer frames, based on the discretized Szego kernel. We use a notion of a Banach frame which generalizes the concept of the Duffin — Shaeffer frame. Having constructed a Banach frame, we can say that any function from the Hardy space can be represented as a series of discretized kernels.