Abstract
On the real line we consider singular integral operators with a linear Carleman shift and complex conjugation, acting in \( \tilde{L}_2(\mathbb{R})\), the real space of all Lebesgue measurable complex value functions on ℝ with p = 2 power. We show that the original singular integral operator with shift and conjugation is, after extension, equivalent to a singular integral operator without shift and with a 4 × 4 matrix coefficients. By exploiting the properties of the factorization of the symbol of this last operator, it is possible to describe the solution of a generalized Riemann boundary value problem with a Carleman shift.
Mathematics Subject Classification (2010). Primary: 47G10; Secondary: 47A68.
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Dedicated to Professor V.G. Kravchenko on the occasion of his seventieth birthday..
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Campos, L.F., Lebre, A.B., Rodríguez, J.S. (2014). On some Generalized Riemann Boundary Value Problems with Shift on the Real Line. In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes Rodríguez, A., Treil, S. (eds) Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, vol 236. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0648-0_6
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DOI: https://doi.org/10.1007/978-3-0348-0648-0_6
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