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 $m_0$ of a scaling function. Then we find conditions on the masks $m_0, m_1,\ldots  , m_q$ under which the corresponding wavelet functions $\psi_1, \psi_2,\ldots  ,\psi_q$ 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.

tight wavelet frames, zero-dimensional groups, refinable functions, trees, unitary extension principle