Abstract
In this chapter we study the mapping properties of periodic integral operators between Sobolev spaces H λ. On the basis of those we prove the well-posedness of periodic integral equations between Sobolev spaces H λ and H λ-α, λ ∈ ℝ, where α is the order of the equation. Corresponding Theorems 6.3.1 and 6.6.1 will be later repeatedly quoted designing approximate methods to solve the problem. In the end of the chapter we study the analyticity of the solution of the integral equation with the analytic coefficient functions and right hand term; these results are new, Section 6.7 is the first publication on this topic. As we will see in Chapters 8–12, the analyticity of the solution enables to prove the exponential convergence of Galerkin, collocation and quadrature methods.
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© 2002 Springer-Verlag Berlin Heidelberg
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Saranen, J., Vainikko, G. (2002). Periodic Integral Equations. In: Periodic Integral and Pseudodifferential Equations with Numerical Approximation. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04796-5_6
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DOI: https://doi.org/10.1007/978-3-662-04796-5_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07538-4
Online ISBN: 978-3-662-04796-5
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