论文标题
the的链序列和零件的零r_ {ii} $类型的复发关系
Chain sequences and Zeros of a perturbed $R_{II}$ type recurrence relation
论文作者
论文摘要
在此手稿中，正交多项式的新代数和分析方面满足$ r_ {ii} $ type type type recurstrence Relience Relience \ begin {align*} \ Mathcal {p} _ {p} _ {n+1} （x-a_n）（x-b_n）\ Mathcal {p} _ {n-1}（x），\ quad n \ geq 0，\ end {align*}，其中$λ_n$是正链序列，$ a_n $，$ a_n $，$ b_n $，$ b_n $，$ c_n $是$ c_n $ sequines con c_n $ sequess a $ c_n $} $} = 0 $和$ \ MATHCAL {P} _0（X）= 1 $，当复发系数受到干扰时。具体而言，在给出了具有零的交织和单调性属性的原始扰动多项式（$ r_ {ii} $ type）的新扰动多项式的表示。对于有限的扰动，使用转移矩阵方法来获得新的结构关系。分析了相应的链序列中共脱毛及其对单位圆的后果的影响。还研究了称为互补链序列的相应链序列中的特定扰动及其对相应Verblunsky系数的影响。
In this manuscript, new algebraic and analytic aspects of the orthogonal polynomials satisfying $R_{II}$ type recurrence relation given by \begin{align*} \mathcal{P}_{n+1}(x) = (x-c_n)\mathcal{P}_n(x)-λ_n (x-a_n)(x-b_n)\mathcal{P}_{n-1}(x), \quad n \geq 0, \end{align*} where $λ_n$ is a positive chain sequence and $a_n$, $b_n$, $c_n$ are sequences of real or complex numbers with $\mathcal{P}_{-1}(x) = 0$ and $\mathcal{P}_0(x) = 1$ are investigated when the recurrence coefficients are perturbed. Specifically, representation of new perturbed polynomials (co-polynomials of $R_{II}$ type) in terms of original ones with the interlacing and monotonicity properties of zeros are given. For finite perturbations, a transfer matrix approach is used to obtain new structural relations. Effect of co-dilation in the corresponding chain sequences and their consequences onto the unit circle are analysed. A particular perturbation in the corresponding chain sequence called complementary chain sequences and its effect on the corresponding Verblunsky coefficients is also studied.
