нуль-мерные группы

On Differential Operator in Compact Zero-dimensional Groups

Authors: Kruss Y. S.

We define strong derivative on zero-dimensional compact group and find conditions under which the differential operator does not depend from an orthonormal system that defines this derivative. For multidimensional case we find conditions under which the differential operator does not depend from method of conversion multidimensional group in one-dimensional group. We obtain a clear view of annihilators in a multidimensional compact zero-dimensional group.

Matrix representation of dilation operator on the product of zero-dimensional locally compact Abelian groups

Authors: Lukomskii S. F.

In the real wavelet analysis dd-dimensional dilation operator may be written with the help of an integer-valued d×dmatrix. We find the matrix representation of the dilation operator on the product of zero-dimensional locally compact Abelian groups.