Orthogonal structure on a quadratic curve
Orthogonal structure on a quadratic curve
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二次曲线上的正交结构
DOI：
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发表时间：
2018
影响因子：
2.1
通讯作者：
Yuan Xu
中科院分区：
文献类型：
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作者：
S. Olver;Yuan Xu
研究了平面上二次曲线上的正交多项式。其中包括椭圆、抛物线、双曲线和两条直线上的正交多项式。对于定义在任意二次曲线上的关于适当权函数的积分，利用两族一元正交多项式构造了一个显式的正交多项式基。文中还研究了每种情况下傅里叶正交展开式的收敛问题。我们讨论了傅里叶延拓问题、奇点或近奇点函数的插值法以及具有不可微势或近不可微势的薛定谔方程的解的应用。
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas and two lines. For an integral with respect to an appropriate weight function defined on any quadratic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. Convergence of the Fourier orthogonal expansions is also studied in each case. We discuss applications to the Fourier extension problem, interpolation of functions with singularities or near singularities and the solution of Schrödinger’s equation with nondifferentiable or nearly nondifferentiable potentials.