I. V. Baibulov, “On the representations of the <nobr>$C^*$</nobr>-algebra of singular integral operators on a complex contour with discontinuous semi-almost periodic coefficients”, Izv. RAN. Ser. Mat., 2025, Volume 89, Issue 6,Pages <nobr>45

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On the representations of the $C^*$-algebra of singular integral operators on a complex contour with discontinuous semi-almost periodic coefficients

I. V. Baibulov

Saint Petersburg State University

Abstract: A $C^*$-algebra generated by one-dimensional singular integral operators on an unbounded complex contour is studied. The coefficients are allowed to have jump discontinuities at the contour points and stabilize to almost periodic functions on each arc extending to infinity. All primitive ideals of this algebra are listed.

Keywords: singular integral operator, complex contour, semi-almost periodic coefficients, spectrum of a $C^*$-algebra, primitive ideals, localization principle.

UDC: 517.986.32+517.983.34

MSC: 47G10, 47L80, 42A75

Received: 22.10.2024
Revised: 18.03.2025

DOI: 10.4213/im9665