Abstract
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.
Partially supported by NSF Grant DMS-91-01143
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Dedicated to Harold Widom on the occasion of his 60th birthday
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Karlovich, Y., Spitkovsky, I. (1994). (Semi)-Fredholmness of Convolution Operators on the Spaces of Bessel Potentials. In: Basor, E.L., Gohberg, I. (eds) Toeplitz Operators and Related Topics. Operator Theory Advances and Applications, vol 71. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8543-0_9
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