论文标题
飞机与标量正交的矩阵正交性在黎曼表面
Matrix orthogonality in the plane versus scalar orthogonality in a Riemann surface
论文作者
论文摘要
我们考虑在复杂平面上的轮廓上的非高矩阵正交性。鉴于可对角和理性的矩阵值的重量，我们表明基督佛教 - darboux（CD）内核是根据矩阵正交多项式构建的，等于在Riemann表面中重现了Meromormormormormorphiq函数的标量值。如果此Riemann表面具有$ 0 $的属，则基质值CD内核等效于平面中多项式的标量繁殖核。有趣的是，这种标量复制核不一定是标量CD内核。作为我们结果的应用，我们表明某些双重周期性润热瓷砖模型的相关内核允许仅涉及标量CD内核的双轮廓积分表示。这简化了Duit和Kuijlaars的公式。
We consider a non-Hermitian matrix orthogonality on a contour in the complex plane. Given a diagonalizable and rational matrix valued weight, we show that the Christoffel--Darboux (CD) kernel, which is built in terms of matrix orthogonal polynomials, is equivalent to a scalar valued reproducing kernel of meromorphic functions in a Riemann surface. If this Riemann surface has genus $0$, then the matrix valued CD kernel is equivalent to a scalar reproducing kernel of polynomials in the plane. Interestingly, this scalar reproducing kernel is not necessarily a scalar CD kernel. As an application of our result, we show that the correlation kernel of certain doubly periodic lozenge tiling models admits a double contour integral representation involving only a scalar CD kernel. This simplifies a formula of Duits and Kuijlaars.
