Wavelet frames on the sets of $M$-positive vectors

Wavelets on the spaces of $M$-positive vectors are studied. Such a space is a multidimensional analog of the half-line in Walsh analysis. Similarly to the half-line, there exists a class of so-called test functions (with a compact support of the function itself and of its Fourier transform) in such spaces. Wavelet frames consisting of the test functions are of special interest because they may be useful for applications to signal processing. A method for constructing such dual wavelet frames is developed in the paper.