Let A be an appropriate planar domain and let f be a piecewise smooth function on R-2. We discuss the rate of convergence of S(lambda)f(x) = integral(lambdaA) (f) over cap(xi)exp(2piixi (.) x)dxi in terms of the interaction between the geometry of A and the geometry of the singularities of f. The most subtle case is when x belongs to the singular set of f
Brandolini, L., Colzani, L., Iosevich, A., Travaglini, G. (2002). The rate of convergence of Fourier expansions in the plane: a geometric viewpoint. MATHEMATISCHE ZEITSCHRIFT, 242(4), 709-724 [10.1007/s002090100375].
The rate of convergence of Fourier expansions in the plane: a geometric viewpoint
COLZANI, LEONARDO;TRAVAGLINI, GIANCARLO
2002
Abstract
Let A be an appropriate planar domain and let f be a piecewise smooth function on R-2. We discuss the rate of convergence of S(lambda)f(x) = integral(lambdaA) (f) over cap(xi)exp(2piixi (.) x)dxi in terms of the interaction between the geometry of A and the geometry of the singularities of f. The most subtle case is when x belongs to the singular set of f
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