Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Zur, Jan"'
Autor:
Sète, Olivier, Zur, Jan
We give sufficient conditions under which a polyanalytic polynomial of degree $n$ has (i) at least one zero, and (ii) finitely many zeros. In the latter case, we prove that the number of zeros is bounded by $n^2$. We then show that for all $k \in \{0
Externí odkaz:
http://arxiv.org/abs/2403.04591
Autor:
Sète, Olivier, Zur, Jan
Publikováno v:
IMA Journal of Numerical Analysis, Volume 42(3), 2022, pp. 2403-2428
We present a continuation method to compute all zeros of a harmonic mapping $f$ in the complex plane. Our method works without any prior knowledge of the number of zeros or their approximate location. We start by computing all solution of $f(z) = \et
Externí odkaz:
http://arxiv.org/abs/2011.00079
Autor:
Sète, Olivier, Zur, Jan
Publikováno v:
Annales Fennici Mathematici, 46(1) (2021), 225-247
We derive a formula for the number of pre-images under a non-degenerate harmonic mapping $f$, using the argument principle. This formula reveals a connection between the pre-images and the caustics. Our results allow to deduce the number of pre-image
Externí odkaz:
http://arxiv.org/abs/1908.08759
Autor:
Sète, Olivier, Zur, Jan
Publikováno v:
IMA Journal of Numerical Analysis, Volume 40(4), 2020, pp. 2777-2801
We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton's method for analytic functions. The complex formulation of the method allows an analysis in a complex variables spirit. For z
Externí odkaz:
http://arxiv.org/abs/1901.05242
Autor:
Liesen, Jörg, Zur, Jan
Publikováno v:
Comput. Methods Funct. Theory 18(3) (2018), 463--472
Generalizing several previous results in the literature on rational harmonic functions, we derive bounds on the maximum number of zeros of functions $f(z) = \frac{p(z)}{q(z)} - \overline{z}$, which depend on both $\mathrm{deg}(p)$ and $\mathrm{deg}(q
Externí odkaz:
http://arxiv.org/abs/1706.04102
Autor:
Liesen, Jörg, Zur, Jan
Publikováno v:
Comput. Methods Funct. Theory 18(4) (2018), 583--607
We study the effect of constant shifts on the zeros of rational harmomic functions $f(z) = r(z) - \conj{z}$. In particular, we characterize how shifting through the caustics of $f$ changes the number of zeros and their respective orientations. This a
Externí odkaz:
http://arxiv.org/abs/1702.07593
Autor:
Zur, Jan
In this doctoral thesis, we consider the zeros of harmonic mappings in the complex plane. Our study was originally motivated by the theory of gravitational lensing in astrophysics, where special cases of such functions and their zeros play an importa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2fffef98b69488eb2a098107cfc97334
Akademický článek
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Autor:
Sète, Olivier, Zur, Jan
Publikováno v:
IMA Journal of Numerical Analysis; Jul2022, Vol. 42 Issue 3, p2403-2428, 26p
Akademický článek
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