非平稳Ruijsenaars函数的基本性质
Basic Properties of Non-Stationary Ruijsenaars Functions
摘要：
对于任意变量，最近引入了一个非平稳的Ruijsenaars函数作为三角Ruijsenaars模型的一个显式渐近自由解的自然推广，并证明了这个非平稳的Ruijsenaars函数提供了椭圆Ruijsenaars模型的一个显式解.我们提出了替代系列表示的非平稳Ruijsenaars函数，我们证明了这些系列收敛。我们还介绍了新的差分算子称为${\mathcal T}$，我们证明在三角极限和猜想在一般情况下，对角作用的非平稳Ruijsenaars函数。
英文摘要：
For any variable number, a non-stationary Ruijsenaars function was recently introduced as a natural generalization of an explicitly known asymptotically free solution of the trigonometric Ruijsenaars model, and it was conjectured that this non-stationary Ruijsenaars function provides an explicit solution of the elliptic Ruijsenaars model. We present alternative series representations of the non-stationary Ruijsenaars functions, and we prove that these series converge. We also introduce novel difference operators called ${\mathcal T}$ which, as we prove in the trigonometric limit and conjecture in the general case, act diagonally on the non-stationary Ruijsenaars functions.
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