(Semi)-Fredholmness of Convolution Operators on the Spaces of Bessel Potentials

The consideration of above mentioned operators on the union of intervals and/or rays is reduced to the canonical situation of operators W k on L P (ℝ+) with semi almost periodic presymbols K at the expense of inflating the size of K. The Fredholm theory (that is, conditions of n-, d-normality and the index formula) is developed. In particular, relations between (semi-)Fredholmness of W K , invertibility of $${W_{{k_ \pm }}}$$ with K ± being almost periodic representatives of K at ±∞, and factorability of K ± are established.