Dyadic distributions

Abstract

On the basis of the concept of pointwise dyadic derivative dyadic distributions are introduced as continuous linear functionals on the linear space of infinitely differentiable functions compactly supported by the positive half-axis together with all dyadic derivatives. The completeness of the space of dyadic distributions is established. It is shown that a locally integrable function on generates a dyadic distribution. In addition, the space of infinitely dyadically differentiable functions on rapidly decreasing in the neighbourhood of is defined. The space of dyadic distributions of slow growth is introduced as the space of continuous linear functionals on . The completeness of the space is established; it is proved that each integrable function on with polynomial growth at generates a dyadic distribution of slow growth. Bibliography: 25 titles.