Noetherian solvability of an operator singular integral equation with a Carleman shift in fractional spaces

Abstract

In this paper, we obtain conditions of Noetherian solvability and the Index formula for a singular integral equation with a Cauchy kernel and a Carleman shift in Besov space, which is embedded into the space of continuous functions on a closed Lyapunov contour but not into the class of functions satisfying Hölder condition.

Keywords:

• Noetherian solvability
• singular integral equation
• Carleman shift
• Besov spaces

AMS Subject Classifications:

• 30H25
• 30H05
• 30H25
• 45E05
• 30E20

Acknowledgments

The authors thank the anonymous referees for reading the paper carefully and providing thoughtful comments, which improved the exposition of the paper and for bringing reference [11] to their attention.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan [grant number AP05133283].