Asymptotics for the Zeros and Poles of Normalized Pad E Approximants to E Z

Padé Approximants in Complex Points Revisited

In 1976, Chisholm et al. 1 published a paper concerning the location of poles and zeros of Padé approximants of ln 1 − z developed at the complex point ζ : ln 1 − z ln 1 − ζ − ∑∞ n 1 1/n z − ζ/1 − ζ . They claimed that all poles and zeros of diagonal Padé approximants n/n interlace on the cut z ζ t 1 − ζ , t ∈ 1,∞ . Unfortunately, this result is only partially true, for poles. Klarsfeld remarke...

Pad E Type Approximants with Preassigned Zeros

Inequalities for the polar derivative of a polynomial with $S$-fold zeros at the origin

‎Let $p(z)$ be a polynomial of degree $n$ and for a complex number $alpha$‎, ‎let $D_{alpha}p(z)=np(z)+(alpha-z)p'(z)$ denote the polar derivative of the polynomial p(z) with respect to $alpha$‎. ‎Dewan et al proved‎ ‎that if $p(z)$ has all its zeros in $|z| leq k, (kleq‎ ‎1),$ with $s$-fold zeros at the origin then for every‎ ‎$alphainmathbb{C}$ with $|alpha|geq k$‎, ‎begin{align*}‎ ‎max_{|z|=...

The diagonal of the Pad e table andthe approximation of the Weyl functionof second order di erence

We study connections between diagonal Pad e approximants and spectral properties of second order diierence operators with complex coeecients. In a rst part, we identify the diagonal of the Pad e table with a particular diierence operator which is shown to have maximal resolvent set. The spectrum of an asymptotically periodic complex diierence operator is given, and we prove convergence on the r...

Strong asymptotics of orthogonal polynomials with varying measures and Hermite–Pad e approximants

The strong asymptotic behaviour of orthogonal polynomials with respect to a general class of varying measures is given for the case of the unit circle and the real line. These results are used to obtain certain asymptotic relations for the polynomials involved in the construction of Hermite–Pad e approximants of a Nikishin system of functions. c © 1998 Elsevier Science B.V. All rights reserved....