Kergin interpolation in Banach spaces

@article{Petersson2002KerginII,
  title={Kergin interpolation in Banach spaces},
  author={H. Petersson},
  journal={Studia Mathematica},
  year={2002},
  volume={153},
  pages={101-114}
}
We study the Kergin operator on the space HNb(E) of nuclearly entire functions of bounded type on a Banach space E. We show that the Kergin operator is a projector with interpolating properties and that it preserves homogeneous solutions to homogeneous differential operators. Further, we show that the Kergin operator is uniquely determined by these properties. We give error estimates for approximating a function by its Kergin polynomial and show in this way that for any given bounded sequence… Expand
Kergin approximation in Banach spaces
  • Scott Simon
  • Computer Science, Mathematics
  • J. Approx. Theory
  • 2008
Set-valued Hermite interpolation
Polynomial projectors preserving homogeneous partial differential equations

References

SHOWING 1-9 OF 9 REFERENCES
A Constructive Approach to Kergin Interpolation in R(k).
Complex Mean-Value Interpolation and Approximation of Holomorphic Functions
Complex Kergin Interpolation
Infinite dimensional holomorphy in the ring of formal power series: partial differential operators
Complex Analysis on Infinite Dimensional Spaces
Convolution equations for vector-valued entire functions of nuclear bounded type
On the convergence of interpolating polynomials for entire functions
Convolution operators and holomorphic mappings on a Banach space
Differenzenrechnung
  • Deutscher Verlag der Wiss.
  • 1958