Unitary extension principle on zero-dimensional locally compact groups

In this article, we obtain methods for constructing step tight frames on an arbitrary locally compact zero-dimensional group. To do this, we use the principle of unitary extension. First, we indicate a method for constructing a step scaling function on an arbitrary zero dimensional group. To construct the scaling function, we use an oriented tree and specify the conditions on the tree under which the tree generates the mask ������0 of a scaling function. Then we find conditions on the masks ������0, ������1, ... , ������q under which the corresponding wavelet functions 01, 02, ... ,0q generate a tight frame. Using these conditions, we indicate a way of constructing such masks. In conclusion, we give examples of the construction of tight frames.