Abstract
A space of periodic generalised functions, called boehmians, is investigated. The space of boehmians contains all periodic distributions. It is known that not every hyperfunction is a boehmian. We show that the converse is also true. We present some theorems which give sufficient conditions for a sequence of complex numbers to be the Fourier coefficients of a boehmian. Sufficient conditions (in terms of the Fourier coefficients) are obtained for a sequence of boehmians to converge. As an application, a Dirichlet problem is discussed.
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