Opuscula Mathematica

Opuscula Math.
, no. 1
 (), 149-160
Opuscula Mathematica

On some application of biorthogonal spline systems to integral equations

Abstract. We consider an operator \(P_N: L_p(I) \to S_n(\Delta_N)\), such that \(P_Nf=f\) for \(f\in S_n(\Delta_N)\), where \(S_n(\Delta_N)\) is the space of splines of degree \(n\) with respect to a given partition \(\Delta_N\) of the interval \(I\). This operator is defined by means of a system of step functions biorthogonal to \(B\)-splines. Then we use this operator to approximation to the solution of the Fredholm integral equation of the second kind. Convergence rates for the approximation of the solution of this equation are given.
Keywords: operator associated with step functions, \(B\)-splines, integral equation, approximation.
Mathematics Subject Classification: 41A15, 45B05, 45L10, 65R20.
Cite this article as:
Zygmunt Wronicz, On some application of biorthogonal spline systems to integral equations, Opuscula Math. 25, no. 1 (2005), 149-160
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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