The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (1074 KB) | Metadata | Table of Contents | ZAA summary
Volume 13, Issue 2, 1994, pp. 329–345
DOI: 10.4171/ZAA/510

Published online: 1994-06-30

Spline Approximation Methods Cutting Off Singularities

Steffen Roch[1]

(1) Technische Hochschule Darmstadt, Germany

The topic of this paper is some types of singular behavior of spline approximation methods for one-dimensional singular integral operators which are caused by discontinuities in the coefficients or by non-smooth geometries of the underlying curves. These singularities can be cutted off by a modification of the approximation method which is closely related to the finite or infinite section method for discrete Toeplitz operators. Using Banach algebra techniques, one can derive stability criteria for a large variety of modified methods (including Galerkin, collocation, and qualocation.

Keywords: Spline approximation methods, singular integral operators, Mellin operators

Roch Steffen: Spline Approximation Methods Cutting Off Singularities. Z. Anal. Anwend. 13 (1994), 329-345. doi: 10.4171/ZAA/510