Year 2022/2023
| No 134 | October 5th, 2022 |
Spotkanie organizacyjne | ||
| No 135 | October 12th, 2022 |
Jerzy Szczepański Aproksymacja wielomianowa funkcji regularnych w sensie Cullena | ||
| No 136 | October 19th, 2022 |
Jerzy Szczepański Aproksymacja wielomianowa funkcji regularnych w sensie Cullena (kontynuacja) | ||
| No 137 | October 26th, 2022 |
Leokadia Białas-Cież Zastosowania twierdzenia Rouchego w badaniu stabilności wielomianów | ||
| No 138 | November 9th, 2022 |
Beata Deręgowska O oszacowaniu absolutnych stalych projekcji | ||
| No 139 | November 16th, 2022 |
Grzegorz Lewicki Kilka rezultatow o relatywnych stalych projekcji | ||
| No 140 | November 23rd, 2022 |
Grzegorz Lewicki Kilka rezultatow o relatywnych stalych projekcji - kontynuacja | ||
| No 141 | December 7th, 2022 |
Jerzy Szczepański Activities of the Polish Academy of Arts and Sciences for education We present the activities of the members of the Polish Academy of Arts and Sciences for mathematical education in the years 1919-1952 and their continuation in the years 2001-2022. | ||
| No 142 | December 14th, 2022 |
Dimitrios Vavitsas Cyclic polynomials in Dirichlet-type spaces in the unit ball of C^2 The three classical Hilbert spaces of holomorphic functions in the unit ball are the Hardy, Bergman and Dirichlet spaces. All of them are special cases of a space family that depends on a real parameter, called Dirichlet-type spaces. Given a fixed parameter $a\in\mathbb{R}$ the Dirichlet-type space, denoted by $D_a(B_2)$, consists of holomorphic functions $f(z, w) =\sum_{k,l=0}^\infty a_{k,l}z^kw^l$ such that $\sum_{k,l=0}^\infty (2+k+l)^a k!l![(1+k+l)!]^{-1}|a_{k,l}|^2<\infty$. We characterize polynomials that are cyclic for the continuous linear operators $\{S_1, S_2\}$ induced by multiplication by the coordinate functions: $S_i: f\mapsto z_i\cdot f$, called shift operators. The full characterization follows: let $p\in \mathbb{C}[z, w]$ be an irreducible polynomial non-vanishing in the unit ball. If $a\leq 3/2$, then $p$ is cyclic in $D_a(B_2)$. If $3/2< a\leq 2$, then $p$ is cyclic in $D_a(B_2)$ if and only if it has finitely many zeros or it has no zeros in the unit sphere. If $a>3/2$, then p is cyclic if and only if it has no zeros in the unit sphere. | ||
| No 143 | January 11th, 2023 |
Organizational meeting | ||
| No 144 | January 18th, 2023 |
Krzysztof Maciaszek Geometry of uniqueness varieties for a three-point Pick problem in the tridisc Abstract. In this talk we will present a special class of two-dimensional algebraic subvarieties $M_a$ of the unit tridisc, dened as the sets $${(z_1, z_2, z_3) \in D^3: a_1z_1 + a_2z_2 + a_3z_3 = \overline{a_1}z_2z_3 +\overline{a_2}z_3z_1+\overline{a_3}z_1z_2}$$. We will discuss motivations to study this family, its connection to the 3-point Pick interpolation and will describe several geometric properties of $M_a$. We will also sketch the proof of the biholomorphic equivalence between any two surfaces $M_a$ and $M_b$, where the triples $a$ and $b$ satisfy the so called triangle inequality. | ||
| No 145 | March 8th, 2023 |
Benedikt Magnússon Polynomials with exponents in compact convex sets and associated weighted extremal functions Abstract. The usual grading of polynomials uses the unit simplex, i.e. polynomials of degree n have exponents in an n fold dilation of the unit simplex. It is interesting to see what changes when the simplex is replaced by a general compact convex body, especially from the viewpoint of pluripotential theory. Polynomials (with the usual grading) are closely connected to pluripotential theory, e.g. in connection with extremal functions and approximations. Many of these connections can be generalized to polynomials with more general grading, but often with restrictions on the convex body. In particular we will consider characterization of polynomials by L^2 estimates. | ||
| No *** | March 15th, 2023 |
Day of the Faculty of Mathematics and Computer Science (no meeting) | ||
| No 146 | March 22nd, 2023 |
Grzegorz Lewicki On a forgotten theorem of A. Pełczyński | ||
| No 147 | March 29th, 2023 |
Dimitri Jordan Kenne Transfinite diameter of Bernstein sets | ||
| No 148 | April 5th, 2023 |
Tomasz Kobos On the dimension of the set of minimal projections | ||
| No 149 | April 12th, 2023 |
Małgorzata Stawiska-Friedland (AMS/Mathematical Reviews) A certain eigenvector-eigenvalue relation from the viewpoint of exterior algebra Abstract: In 2019 Denton, Parker, Tao and Zhang proved an identity expressing coordinates of eigenvectors of Hermitian matrices solely in terms of the corresponding eigenvalues. The identity generated considerable interest and discussion within the mathematical community, and it turned out it was discovered and re-discovered multiple times, the first time in 1834 by Jacobi. In this talk we will prove our own version of this identity. We consider arbitrary square matrices over $\mathbb{C}$ and allow eigenvalues of multiplicity greater than 1, and prove that the identity in question holds for eigenvectors associated to the eigenvalue $\lambda$ holds if and only if the geometric multiplicity of $\lambda$ equals its algebraic multiplicity. In the proof we use exterior algebra. The approach is accessible to advanced students. | ||
| No 150 | April 19th, 2023 |
Agnieszka Kowalska (Pedagogical University of Cracow) Bernstein-Chebyshev inequality and Baran's radial extremal function on algebraic sets | ||
| No 151 | On Friday, May 12th, 2023 |
Tomasz Beberok (ANS Tarnów) L^p Markov exponent of certain UPC sets | ||
| No 152 | May 17th, 2023 |
Przemysław Sprus On polynomial Julia sets Abstract. The aim of this talk is to present the basic foundations of the theory of iteration of complex polynomials. We will discuss the properties of Julia sets and use some of them in proofs of facts about the shape of Julia sets of quadratic polynomials. We will also mention some results concerning convex hulls of these sets. References: A. F. Beardon, P. J. Rippon, A remark on the shape of quadratic Julia sets, Nonlinearity 7, 1277-1280, (1994) and https://doi.org/10.1090/proc/15224 | ||
| No 153 | May 31st, 2023 |
Álfheidur Edda Sigurdardóttir Weighted pluripotential theory with respect to convex sets Abstract: A polynomial is of degree m if its exponents are contained in the m-th dilate of the unit simplex. If the unit simplex is replaced by any compact convex set, we obtain a new grading of the polynomial ring. We work with a Siciak function with respect to the new grading. That function generally has different growth that logrithmic, so we work with a Siciak-Zakharyuta/pluricomplex Green- function with matching growth, and see when we have equality, i.e. a Siciak-Zakharyuta theorem. This was content from the preprint https://arxiv.org/abs/2305.08260 (and https://arxiv.org/abs/2305.04779) | ||
| No 154 | June 7th, 2023 |
Bergur Snorrason Growth of plurisubharmonic functions and multivariate polynomials Abstract. A common tool in pluripotential theory are extremal functions. One type of extremal functions are the Siciak-Zakharyuta functions. The Bernstein-Walsh theorem describes how these functions relate analytic continuation to polynomial approximations. The subject of discussion will be a generalization of the Siciak-Zakharyuta extremal function which leads to a generalization of the Bernstein-Walsh theorem. This generalization is achieved by focusing on plurisubharmonic functions that grow like logarithmic supporting functions of a convex compact set, instead of simply considering logarithmic growth. | ||
| No 155 | June 14th, 2023 |
Izabela Mandla Pewne uogólnienie rezultatu Benko i Totika o wielomianach ekstremalnych |