Abstract
We derive the Fourier integral associated with the complex Martin function in the Denjoy domain of the Widom type with the Direct Cauchy Theorem (DCT). As an application we study canonical systems and corresponding transfer matrices generated by reflectionless Weyl-Titchmarsh functions in such domains. The DCT property appears to be crucial in many aspects of the underlying theory.
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Acknowledgment
The author would like to express his gratitude to Benjamin Eichinger and Roman Bessonov for very helpful discussions. This work was supported by the Austrian Science Fund FWF, project no: P29363-N32.
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In the study of mathematics, there is a grave injustice: we put in so much effort, but we get such miserable results…
Larry Zalcman (from a private conversation)
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Yuditskii, P. Direct Cauchy theorem and Fourier integral in Widom domains. JAMA 141, 411–439 (2020). https://doi.org/10.1007/s11854-020-0122-7
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DOI: https://doi.org/10.1007/s11854-020-0122-7