Abstract
Semi-almost periodic (SAP) symbols constitute one of the simplest classes of symbols with discontinuities beyond jumps, and as shown in Chapter 1, SAP symbols emerge naturally in several settings. Armed with the results on C+H∞,PC, and AP symbols established in Chapter 2, we here present Sarason’s theory of semi-Fredholmness for scalar Wiener-Hopf operators with SAP symbols. A key result in the analysis of the matter is Sarason’s lemma, which says that the product of an almost periodic function in H∞ with mean value zero and a function in C(S)is a function in C+H∞. Our approach is different from Sarason’s, which can be characterized as an elegant combination of localization techniques and C* -algebra arguments. We rather follow Duduchava and Saginashvili, who gave a proof of Sarason’s theorem that can be carried over to the LP case without undue difficulty.
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© 2002 Springer Basel AG
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Böttcher, A., Karlovich, Y.I., Spitkovsky, I.M. (2002). Scalar Wiener-Hopf Operators with SAP Symbols. In: Convolution Operators and Factorization of Almost Periodic Matrix Functions. Operator Theory: Advances and Applications, vol 131. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8152-4_3
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DOI: https://doi.org/10.1007/978-3-0348-8152-4_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9457-9
Online ISBN: 978-3-0348-8152-4
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