Abstract
In this chapter, we deal with the problem of inversion of the operators S acting in the space L 2(0, ω) and having the form \( Sf = \frac{\rm{d}}{{\rm{d}}{x}} \int\limits_{0}^{\omega} {s(x - t)f(t){\rm{d}}t,} \ f(x) \in {L}^{2}(0, \omega)\) where \( s(x) \in L^{2}(-\omega, \omega)\) and the function \( g(x) = \int\limits_{0}^{\omega} s(x - t)f(t){\rm{d}}{t}\) is assumed to be absolutely continuous.
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© 2015 Springer International Publishing Switzerland
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Sakhnovich, L.A. (2015). Invertible Operator with a Difference Kernel. In: Integral Equations with Difference Kernels on Finite Intervals. Operator Theory: Advances and Applications, vol 84. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-16489-2_1
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DOI: https://doi.org/10.1007/978-3-319-16489-2_1
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-16488-5
Online ISBN: 978-3-319-16489-2
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