论文标题
Sobolev sierpinski垫片上的正交多项式
Sobolev Orthogonal Polynomials on the Sierpinski Gasket
论文作者
论文摘要
我们在Sierpiński垫圈（$ SG $）上开发了Sobolev正交多项式的理论。这些正交多项式是通过使用Sobolev内部产品的几个概念上的$ sg $上的一组单元素应用于$ sg $上的革兰氏阴性正交过程。在为这些正交多项式建立了一些复发关系后，我们给出了它们的$ l^2 $，$ l^\ infty $和sobolev规范的估计，并研究其渐近行为。最后，我们研究了零集多项式集的属性，并开发了快速的计算工具来探索对正交和插值的应用。
We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket ($SG$). These orthogonal polynomials arise through the Gram-Schmidt orthogonalisation process applied on the set of monomials on $SG$ using several notions of a Sobolev inner products. After establishing some recurrence relations for these orthogonal polynomials, we give estimates for their $L^2$, $L^\infty$ and Sobolev norms, and study their asymptotic behaviour. Finally, we study the properties of zero sets of polynomials and develop fast computational tools to explore applications to quadrature and interpolation.
