Abstract:
A new definition of the derivative of variable order
is given based on the interpolation of derivatives of natural order.
For the joint interpolation of a function and its derivative of variable order,
interpolation operators of Hermite–Fejér type
are constructed in the one-dimensional and multidimensional cases.
Upper bounds for the norms of these operators
in the one-dimensional and multidimensional periodic Sobolev spaces
are obtained.
It is shown that, in the one-dimensional case,
the norm of this operator is bounded.
In the multidimensional case,
the upper bound depends on the ratio of the number of nodes
for each coordinate.
Keywords:derivatives of variable order, interpolation operator of Hermite–Fejér type.
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