Varying weights for orthogonal polynomials with monotonically varying recurrence coefficients

نویسندگان

  • Alexander I. Aptekarev
  • Jeffrey S. Geronimo
  • Walter Van Assche
چکیده

and the coefficients in (1.3), which depend on the parameter N , {an,N : bn,N}n=0, bn,N > 0. ∗The authors acknowledge support from NATO Collaborative linkage grant PST.CLG.979738 and INTAS Research Network 03-51-6637. The first author was supported by grants RFBR-05-01-00522, NSh1551.2003.1, Program No. 1 DMS RAS. The second author was supported by an NSF grant. The third author was supported by FWO project G.0455.04 and OT/04/21 from the K.U.Leuven Research Counsel.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Recurrences and explicit formulae for the expansion and connection coefficients in series of the product of two classical discrete orthogonal polynomials

Suppose that for an arbitrary function $f(x,y)$ of two discrete variables, we have the formal expansions. [f(x,y)=sumlimits_{m,n=0}^{infty }a_{m,n},P_{m}(x)P_{n}(y),] $$‎ ‎x^{m}P_{j}(x)=sumlimits_{n=0}^{2m}a_{m,,n}(j)P_{j+m-n}(x)‎,$$ ‎we find the coefficients $b_{i,j}^{(p,q,ell‎ ,‎,r)}$ in the expansion‎ $$‎ ‎x^{ell }y^{r},nabla _{x}^{p}nabla _{y}^{q},f(x,y)=x^{ell‎ ‎}y^{r}f^{(p,q)}(x,y) =sumli...

متن کامل

The asymptotic behaviour of recurrence coefficients for orthogonal polynomials with varying exponential weights

We consider orthogonal polynomials {pn,N(x)}n=0 on the real line with respect to a weight w(x) = e (x) and in particular the asymptotic behaviour of the coefficients an,N and bn,N in the three term recurrence xπn,N (x) = πn+1,N (x)+bn,Nπn,N (x)+an,Nπn−1,N (x). For one-cut regular V we show, using the Deift-Zhou method of steepest descent for Riemann-Hilbert problems, that the diagonal recurrenc...

متن کامل

Orthogonal polynomials with respect to varying weights 1

In this paper we review a connection of orthogonal polynomials with respect to varying weights to weighted approximation, multipoint Pad6 approximation and to some questions of theoretical physics. (~) 1998 Elsevier Science B.V. All rights reserved.

متن کامل

On Asymptotic Regimes of Orthogonal Polynomials with Complex Varying Quartic Exponential Weight∗

We study the asymptotics of recurrence coefficients for monic orthogonal polynomials πn(z) with the quartic exponential weight exp[−N( 1 2z2 + 14 tz)], where t ∈ C and N ∈ N, N → ∞. Our goal is to describe these asymptotic behaviors globally for t ∈ C in different regions. We also describe the “breaking” curves separating these regions, and discuss their special (critical) points. All these pie...

متن کامل

Asymptotic Zero Distribution of Orthogonal Polynomials with Discontinuously Varying Recurrence Coefficients

The zero distribution of orthogonal polynomials pn,N , n = 0, 1, . . . generated by recurrence coefficients an,N and bn,N depending on a parameter N has been recently considered by Kuijlaars and Van Assche under the assumption that an,N and bn,N behave like a(n/N) and b(n/N), respectively, where a(·) and b(·) are continuous functions. Here, we extend this result by allowing a(·) and b(·) to be ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Journal of Approximation Theory

دوره 150  شماره 

صفحات  -

تاریخ انتشار 2008