Results 21 to 30 of about 267 (174)
Boundary Interpolation by Finite Blaschke Products [PDF]
, 2017 Given $n$ distinct points $t_1,\ldots,t_n$ on the unit circle $\T$ and equally many target values $\f_1,\ldots,\f_n\in\T$, we describe all Blaschke products $f$ of degree at most $n-1$ such that $f(t_i)=\f_i$ for $i=1,\ldots,n$. We also describe the cases where degree $n-1$ is the minimal possible.
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Sections and projections of the outer and inner regularizations of a convex body
Mathematika, Volume 72, Issue 3, July 2026.Abstract We establish new geometric inequalities comparing the volumes of sections and projections of a convex body, whose barycenter or Santaló point is at the origin, with those of its inner and outer regularizations. We also provide functional extensions of these inequalities to the setting of log‐concave functions. Our approach relies on the recent
Natalia Tziotziou
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Finite Blaschke products: a survey
, 2015 30 ...
Garcia, Stephan Ramon +2 more
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Stability of Blaschke products under forward iteration
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract Forward iteration of holomorphic self‐maps generalizes the iteration of a single function in a natural way. This framework arises in complex dynamics, for instance, in the study of wandering domains and in seeking suitable extensions of the Denjoy–Wolff theorem. Here, we consider forward iteration of Blaschke products.
Daniela Kraus +2 more
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Singular perturbations of Blaschke products and connectivity of Fatou components [PDF]
, 2017 The goal of this paper is to study the family of singular perturbations of Blaschke products given by Ba,λ(z)=z3z−a1−a¯z+λz2. We focus on the study of these rational maps for parameters a in the punctured disk D∗ and |λ| small.
Canela Sánchez, Jordi +2 more
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Variants of a theorem of Macbeath in finite‐dimensional normed spaces
Mathematika, Volume 72, Issue 2, April 2026.Abstract A classical theorem of Macbeath states that for any integers d⩾2$d \geqslant 2$, n⩾d+1$n \geqslant d+1$, d$d$‐dimensional Euclidean balls are hardest to approximate, in terms of volume difference, by inscribed convex polytopes with n$n$ vertices.
Zsolt Lángi, Shanshan Wang
wiley +1 more source
Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains
Communications on Pure and Applied Mathematics, Volume 79, Issue 3, Page 762-822, March 2026.Abstract We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplacians in terms of their semiclassical counterpart. We show that the classical inequalities of Berezin–Li–Yau and Kröger, valid for Riesz exponents γ≥1$\gamma \ge 1$, extend to certain values γ<1$\gamma <1$, provided the underlying ...
Rupert L. Frank, Simon Larson
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ON SOME GEOMETRIC PROPERTIES OF FINITE BLASCHKE PRODUCTS
International Electronic Journal of Geometry, 2015 In this paper we consider some geometric properties of finite Blaschke products for the unit disc and for the upper half plane.
Özgür, Nihal Yılmaz, Uçar, Sümeyra
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Quasi‐Fuchsian flows and the coupled vortex equations
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract We provide an alternative construction of the quasi‐Fuchsian flows introduced by Ghys. Our approach is based on the coupled vortex equations that allows to see these flows as thermostats on the unit tangent bundle of the Blaschke metric, uniquely determined by a conformal class and a holomorphic quadratic differential.
Mihajlo Cekić, Gabriel P. Paternain
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Arens Regularity of Banach Function Algebras and Decomposable Blaschke Products whose Degree is a Power of 2 [PDF]
, 2023 This thesis presents three pieces of work. Within the first two thirds of the thesis, we study Arens regularity of Banach algebras. We first study Arens regularity of weighted semigroup algebras that arise from totally ordered semilattices.
Choi, Yemon +2 more
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