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Małgorzata Stawiska

Publications and source records attributed to Małgorzata Stawiska.

10 recordsLinked to original sources
arXiv2026

90+ years of the Scottish Book

Inspired by the recent 90th anniversary of the Scottish Book we present some reflections about its impact. First we discuss new areas of mathematics it helped launch. Then we argue that it was actively used in stimulating the interests and results of junior mathematicians and students. Also, we summarize the progress during the decade that has passed since the publication of [55], which contained a review of solved problems from the Scottish Book. We also provide an overview of collections of open problems related in one way or another to the Scottish Book. All formulations of the Scottish Book problems in English are cited here from Mauldin, Richard Daniel (ed.) 2015: The Scottish Book. Mathematics from the Scottish Café. With selected problems from the New Scottish Book. 2nd updated and enlarged edition. Cham: Birkhäuser/Springer

math.HO↗
arXiv2021

An extremal subharmonic function in non-archimedean potential theory

We define an analog of the Leja-Siciak-Zaharjuta subharmonic extremal function for a proper subset $E$ of the Berkovich projective line $P^1$ over a field with a non-archimedean absolute value, relative to a point $ζ\not \in E$. When $E$ is a compact set with positive capacity, we prove that the upper semicontinuous regularization of this extremal function equals the Green function of $E$ relative to $ζ$. As a separate result, we prove the Brelot-Cartan principle, under the additional assumption that the Berkovich topology is second countable.

math.AG↗
arXiv2019

On a completeness problem in a Fourier-based probability metrics in $\mathbb{R}^N$

We study completeness of the spaces $\mathcal{P}_s^=$ of probability measures in $\mathbb{R}^N$ which have equal (prescribed) moments up to order $s \in \mathbb{N}$, endowed with the metric $d_s(μ,ν)=\sup_{x \in \mathbb{R}^N\setminus 0}\frac{|\hat μ(x)-\hat ν(x)|}{|x|^s}$, where $\hat μ$ is the characteristic function of $μ$. We prove that the spaces $(\mathcal{P}_s^=,d_s)$ are complete if $s$ is even and construct suitable counterexamples to completeness for all odd $s$. This solves an open problem formulated by J. Carrillo and G. Toscani in 2007.

math.PR↗
arXiv2015

Distinguished graduates in mathematics of the Jagiellonian University in the interwar period. Part I: 1918-1926

In this study, we present profiles of some distinguished graduates in mathematics of the Jagiellonian University from the years 1918-1939. We discuss their professional paths and scholarly achievements, instances of scientific collaboration, connections with other academic centers in Poland and worldwide, involvement in mathematical education and teacher training, as well as their later roles in Polish scientific and academic life. We also try to understand in what way they were shaped by their studies and how much of Kraków scientific traditions they continued. We find strong support for the claim that there was a distinct, diverse and deep mathematical stream in Kraków between the wars, rooted in classical disciplines like differential equations and geometry, but also open to new trends in mathematics. Part I concerns the graduates before the university reform, in 1918-1926.

math.HO↗
arXiv2015

Distinguished graduates in mathematics of Jagiellonian University in the interwar period. Part II: 1928-1939

In this study, we continue to present profiles of some distinguished graduates in mathematics of the Jagiellonian University from the years 1918-1939. We discuss their professional paths and scholarly achievements, instances of scientific collaboration, connections with other academic centers in Poland and worldwide, involvement in mathematical education and teacher training, as well as their later roles in Polish scientific and academic life. We also try to understand in what way they were shaped by their studies and how much of Kraków scientific traditions they continued. We find strong support for the claim that there was a distinct, diverse and deep mathematical stream in Kraków between the wars, rooted in classical disciplines like differential equations and geometry, but also open to new trends in mathematics. Part II concerns people who graduated after the university reform, getting the newly introduced master's degree in mathematics, in 1928-39.

math.HO↗
arXiv2014

Lucjan Emil Böttcher and his mathematical legacy

This article concerns the life and work of Lucjan Emil Böttcher (1872-1937), a Polish mathematician. Besides biographical and bibliographical information, it contains a survey of his mathematical achievements in the theory of iteration and holomorphic dynamics. Some documents are presented for the first time.

math.HO↗
arXiv2010

Liouville theorem with parameters: asymptotics of certain rational integrals in differential fields

We study asymptotics of integrals of certain rational functions that depend on parameters in a field $K$ of characteristic zero. We use formal power series to represent the integral and prove certain identities about its coefficients following from generalized Vandermonde determinant expansion. Our result can be viewed as a parametric version of a classical theorem of Liouville. We also give applications.

math.CA↗
arXiv2006

Attracting divisors on projective algebraic varieties

We obtain sufficient and necessary conditions (in terms of positive singular metrics on an associated line bundle) for a positive divisor $D$ on a projective algebraic variety $X$ to be attracting for a holomorphic map $f:X \mapsto X$.

math.CV↗