Hadamard's problem and coxeter groups: New examples of Huygens' equations

@article{Berest1994HadamardsPA,
  title={Hadamard's problem and coxeter groups: New examples of Huygens' equations},
  author={Yuri Yu. Berest and A P Veselov},
  journal={Functional Analysis and Its Applications},
  year={1994},
  volume={28},
  pages={3-12}
}
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References

SHOWING 1-10 OF 24 REFERENCES
Commutative rings of partial differential operators and Lie algebras
We give examples of finite gap Schrödinger operators in the two-dimensional case.
Deformations preserving Huygens’ principle
A new kind of deformation related to the Korteweg–de Vries hierarchy and its master symmetries is studied. The algebra of deformations is generated by trivial (point) transformations via a specialExpand
Shift operators for the quantum Calogero-Sutherland problems via Knizhnik-Zamolodchikov equation
We give a natural interpretation of the shift operators for Calogero-Sutherland quantum problem via KZ equation using Matsuo-Cherednik mappings. The explicit formulas for the inversions of theseExpand
Algebraic integrability for the Schrödinger equation and finite reflection groups
Algebraic integrability of ann-dimensional Schrödinger equation means that it has more thann independent quantum integrals. Forn=1, the problem of describing such equations arose in the theory ofExpand
A Remark on the Dunkl Differential—Difference Operators
Let E be a Euclidean vector space of dimension n with inner product (·,·). For each α ∈ E with (α, α) = 2 we write $$ {r_{\alpha }}(\lambda ) = \lambda - (\alpha, \lambda )\alpha, \lambda \in E $$Expand
The hierarchy of Huygens equations in spaces with a non-trivial conformal group
CONTENTS Introduction Chapter I. The wave equation in curved spaces § 1. Conformal invariance § 2. The geodesic distance § 3. The Cauchy problem § 4. The Huygens principle Chapter II. GeneralizationExpand
Differential-difference operators associated to reflection groups
There is a theory of spherical harmonics for measures invariant under a finite reflection group. The measures are products of powers of linear functions, whose zero-sets are the mirrors of theExpand
Some applications of hypergeometric shift operators
Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons.Expand
The sine‐Gordon equations: Complete and partial integrability
The sine–Gordon equation in one space‐one time dimension is known to possess the Painleve property and to be completely integrable. It is shown how the method of ‘‘singular manifold’’ analysisExpand
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