Discrete integrable systems generated by Hermite-Padé approximants

@inproceedings{Aptekarev2016DiscreteIS,
  title={Discrete integrable systems generated by Hermite-Pad{\'e} approximants},
  author={Alexander I. Aptekarev and Maxim S. Derevyagin and Walter Van Assche},
  year={2016}
}
We consider Hermite-Pade approximants in the framework of discrete integrable systems defined on the lattice . We show that the concept of multiple orthogonality is intimately related to the Lax representations for the entries of the nearest neighbor recurrence relations and it thus gives rise to a discrete integrable system. We show that the converse statement is also true. More precisely, given the discrete integrable system in question there exists a perfect system of two functions, i.e. a… CONTINUE READING

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

References

Publications referenced by this paper.
SHOWING 1-10 OF 30 REFERENCES

Discrete Complex Analysis and Probability

VIEW 1 EXCERPT

P

  • P. E. Spicer, F. W. Nijhoff
  • H. van der Kamp, Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm, Nonlinearity 24
  • 2011
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Perfect systems

  • K. Mahler
  • Compos. Math. 19
  • 1968
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Rational approximants for Euler’s constant and recurrence relations

  • A. I. Aptekarev
  • Proceedings of the Steklov Institute of Mathematics 272
  • 2011
VIEW 1 EXCERPT

Nearest neighbor recurrence relations for multiple orthogonal polynomials

VIEW 4 EXCERPTS