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We consider two indeterminate moment problems: One corresponding to a birth and death process with quartic rates and the other corresponding to the Al-Salam-Carlitz q-polynomials. Using the Darboux… (More)

Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a “minimal” quantization scheme,… (More)

- Henrik Pedersen, Christina Tønnesen–Friedman, Galliano Valent
- 1999

We write an ansatz for quasi-Einstein Kähler metrics and construct new complete examples. Moreover, we construct new compact generalized quasi-Einstein Kähler metrics on some ruled surfaces,… (More)

- Galliano Valent
- 2002

The results obtained by Pauli, in his article published in 1926 on the hydrogen atom, made essential use of the quantum dynamical so(4) symmetry of the bound states. Pauli used this symmetry to… (More)

It is shown that most, but not all, of the four dimensional metrics in the MultiCentre family with integrable geodesic flow may be recognized as belonging to spatially homogeneous Bianchi type A… (More)

In the recent new edition of the collected works of T.J. Stieltjes, one of us gave an impression of the impact of Stieltjes' work a century after his death 43]. In this paper we give an update and… (More)

We present some recent progresses on Heun functions, gathering results from classical analysis up to elliptic functions. We describe Picard’s generalization of Floquet’s theory for differential… (More)

- Mourad E. H. Ismail, Galliano Valent, Gang J. Yoon
- Journal of Approximation Theory
- 2001

We characterize the orthogonal polynomials in a class of polynomials defined through their generating functions. This led to three new systems of orthogonal polynomials whose generating functions and… (More)

- Pierre-Yves Casteill, Evgeny Ivanov, Galliano Valent
- 2001

We construct, using harmonic superspace and the quaternionic quotient approach, a quaternionic-Kähler extension of the most general two centres hyper-Kähler metric. It possesses U(1)×U(1) isometry,… (More)

- Pierre-Yves Casteill, Evgeny Ivanov, Galliano Valent
- 2001

Starting from the generic harmonic superspace action of the quaternion-Kähler sigma models and using the quotient approach we present, in an explicit form, a quaternion-Kähler extension of the double… (More)