TY  - JOUR
ID  - Wronicz2005
LB  - Wronicz2005
AU  - Wronicz, Zygmunt
TI  - On some application of biorthogonal spline systems to integral equations
ST  - On some application of biorthogonal spline systems to integral equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2005
VL  - 25
IS  - 1
SP  - 149
EP  - 160
DO  - http://dx.doi.org/10.7494/OpMath.2005.25.1.149
UR  - http://dx.doi.org/10.7494/OpMath.2005.25.1.149
AB  - 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.
KW  - operator associated with step functions
KW  - \(B\)-splines
KW  - integral equation
KW  - approximation
SN  - 1232-9274
ER  -