28 citations · 117 across the 14 of their papers we have counts for
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Baxter -operator for the hyperbolic Calogero--Moser system
Martin Hallnäs
We introduce a -operator for the hyperbolic Calogero--Moser system as a one-parameter family of explicit integral operators. We establish the standard properties…
Higher order deformed elliptic Ruijsenaars operators
Martin Hallnäs, Edwin Langmann, Masatoshi Noumi +1
We present four infinite families of mutually commuting difference operators which include the deformed elliptic Ruijsenaars operators. The trigonometric limit of this kind of oper…
Quantization and explicit diagonalization of new compactified trigonometric Ruijsenaars-Schneider systems
Tamás F. Görbe, Martin A. Hallnäs
Recently, Fehér and Kluck discovered, at the level of classical mechanics, new compactified trigonometric Ruijsenaars-Schneider -particle systems, with phase space symplectomorp…
Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type. II. The two- and three-variable cases
Martin Hallnäs, Simon Ruijsenaars
In a previous paper we introduced and developed a recursive construction of joint eigenfunctions for the Hamiltonians of the hyperbolic relativistic Calogero-M…
Complex exceptional orthogonal polynomials and quasi-invariance
William A. Haese-Hill, Martin A. Hallnäs, Alexander P. Veselov
Consider the Wronskians of the classical Hermite polynomials where $k_i=λ_i+n-i,…
A product formula for the eigenfunctions of a quartic oscillator
Martin Hallnäs, Edwin Langmann
We consider the Schrödinger operator on the real line with an even quartic potential. Our main result is a product formula of the type $ψ_k(x)ψ_k(y) = \int_{\mathbb{R}} ψ_k(z)\math…
Source identities and kernel functions for deformed (quantum) Ruijsenaars models
F. Atai, M. Hallnäs, E. Langmann
We consider the relativistic generalization of the quantum Calogero-Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic…
Baker-Akhiezer functions and generalised Macdonald-Mehta integrals
M. V. Feigin, M. A. Hallnas, A. P. Veselov
For the rational Baker-Akhiezer functions associated with special arrangements of hyperplanes with multiplicities we establish an integral identity, which may be viewed as a genera…
A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type
Martin Hallnäs, Edwin Langmann
In this paper we consider a large class of many-variable polynomials which contains generalisations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cas…
Explicit formulas for the eigenfunctions of the N-body Calogero model
Martin Hallnäs, Edwin Langmann
We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two…