Abstract
Galerkin’s method with trigonometric polynomials as trial and test functions is used to construct approximate solutions of periodic singular integral equations and pseudo-differential equations. We present results on pointwise rates of convergence, showing amongst other things that if the solution is in (C τ, then the error is O(n −τlog n), where n is the degree of the trigonometric polynomials. This result is the best that can be expected, since the same rate of convergence holds for the partial sums of the Fourier series of a function in C τ.
This research was carried out while the first author was a guest professor at the Universität Stuttgart.
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This paper is dedicated to Professor Dr. I. Gohberg on the occasion of his 60-th birthday.
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© 1989 Birkhäuser Verlag Basel
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McLean, W., Wendland, W.L. (1989). Trigonometric Approximation of Solutions of Periodic Pseudodifferential Equations. In: Dym, H., Goldberg, S., Kaashoek, M.A., Lancaster, P. (eds) The Gohberg Anniversary Collection. Operator Theory: Advances and Applications, vol 41. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9278-0_20
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DOI: https://doi.org/10.1007/978-3-0348-9278-0_20
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