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Mathematical Colloquium of the Bauman Moscow State Technical University
October 15, 2020 17:30, Moscow, Zoom video-meeting
 


Reconstruction of the values of algebraic function via polynomial Hermite–Pade $m$-system

A. V. Komlov

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Abstract: For an arbitrary tuple of $m+1$ analytic germs $[f_0, f_1,\dots, f_m]$ at some point $x_0$ we introduce the polynomial Hermite–Pade $m$-system. For each $n\in\mathbb N$ this system consists of $m$ tuples of polynomials. These tuples are numerated by the number $k=1,\dots,m$. The $k$-th tuple consists of ${m+1}\choose k$ polynomials, which are called "$k$-th polynomials of Hermite–Pade $m$-system" of order $n$. We show, that for the case, when the germs $f_j=f^j$, where $f$ is a germ of some algebraic function of order $m+1$, the ratio of some $k$-th polynomials of Hermite–Pade $m$-system converges (as $n\to\infty$) to the sum of the values of $f$ on first $k$ sheets of so-called Nuttall partition of its Riemann surface into sheets.

Note that the well known Hermite–Pade polynomials of types 1 and 2 are $m$-th and 1-st polynomials of Hermite–Pade $m$-system, respectively.

Zoom-conference identificator: 848 4984 8157; Password: 634324

Website: https://us02web.zoom.us/j/84849848157?pwd=YllFbzdzMlRFZ1Z3aGxhZVJ3UmlYQT09
 
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