## ABSTRACT

In Chapter 4 the small 6-pseudodifferential calculus was used to carry out the (‘symbolic’) construction of a parametrix. This gives an inverse up to errors in the small-residual space, bū* ). The fact that these operators are not generally compact shows that more needs to be done in order to understand the mapping, especially Fredholm, properties of ellip­ tic 6-differential operators. What is required is the inversion of the other symbol, i.e. the indicial operator. The Mellin transform can be applied, so reducing the question to the invertibility properties of the indicial family. For this the symbolic construction is a convenient starting point.