Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Journal of Computational and Applied Mathematics - Special issue on scattered data
Radial Basis Functions
A Duchon framework for the sphere
Journal of Approximation Theory
Lp-error estimates for radial basis function interpolation on the sphere
Journal of Approximation Theory
Meshfree Approximation Methods with MATLAB
Meshfree Approximation Methods with MATLAB
Advances in Computational Mathematics
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This work discusses interpolation of complex-valued functions defined on the positive real axis I by certain special subspaces, in a variational setting that follows the approach of Light and Wayne [W. Light, H. Wayne, Spaces of distributions, interpolation by translates of a basis function and error estimates, Numer. Math. 81 (1999) 415-450]. The set of interpolation points will be a subset {a"1,...,a"n} of I and the interpolants will take the form u(x)=@?i=1n@a"i(@t"a"""i@f)(x)+@?j=0m-1@b"jp"@m","j(x)(x@?I), where @m=-1/2,@f is a complex function defined on I (the so-called basis function), p"@m","j(x)=x^2^j^+^@m^+^1^/^2(j@?Z"+,0@?j@?m-1) is a Muntz monomial, @t"z(z@?I) denotes the Hankel translation operator of order @m, and @a"i,@b"j(i,j@?Z"+,1@?i@?n,0@?j@?m-1) are complex coefficients. An estimate for the pointwise error of these interpolants is given. Some numerical examples are included.