Abstract:
Hermitian-type splines (nonpolynomial in general)
of second order (said to be quasi-Hermitian) are
constructed on irregular grids. Extensions of the system of
functionals which are biorthogonal to such splines are
obtained, necessary and sufficient conditions for continuity of
the splines are established, direct solutions of some generalized
Hermite interpolating problems are given.
The limit space of quasi-Hermitian splines is constructed under the condition
of limiting transition from the spaces of B-splines when pasting together
some knots of the grid.
Keywords:quasi-Hermitian splines, biorthogonal systems, smoothness of splines, interpolation problems, limit spaces of splines.
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