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Related papers: Boundary interpolation by finite Blaschke products

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This paper gives a sharp upper bound for the Betti numbers of a finitely generated multigraded $R$-module, where $R=\Bbbk [x_{1},...,x_{m}]$ is the polynomial ring over a field $\Bbbk$ in $m$ variables. The bound is given in terms of the…

Commutative Algebra · Mathematics 2007-05-23 Amanda Beecher

M. Daher gave conditions so that the spheres of the spaces in the interior of a complex interpolation scale are uniformly homeomorphic. We look for sufficient conditions for the validity of this result and related ones on the extremes of…

Functional Analysis · Mathematics 2024-05-08 Willian Corrêa , Valentin Ferenczi , Rafela Gesing , Pedro Tradacete

Building upon Bennett's and Grosse-Erdmann's ideas falling under the conceptual umbrella of factorization of inequalities, we propose a unified approach towards the structure of certain Banach ideal spaces defined in terms of the least…

Functional Analysis · Mathematics 2024-02-28 Tomasz Kiwerski , Jakub Tomaszewski

These notes answer the question "When can a finite Blaschke product $B$ be written as a composition of two finite Blaschke products $B_1$ and $B_2$, that is, $B=B_1\circ B_2$, in a non-trivial way, that is, where the order of each is…

Complex Variables · Mathematics 2012-07-18 Carl C. Cowen

For oriented connected closed manifolds of the same dimension, there is a transitive relation: $M$ dominates $N$, or $M \ge N$, if there exists a continuous map of non-zero degree from $M$ onto $N$. Section 1 is a reminder on the notion of…

Algebraic Topology · Mathematics 2016-09-22 Pierre de la Harpe

Let $f(x,y)$ be a real polynomial of degree $d$ with isolated critical points, and let $i$ be the index of $grad f$ around a large circle containing the critical points. An elementary argument shows that $|i| \leq d-1$. In this paper we…

alg-geom · Mathematics 2008-02-03 Alan H. Durfee

The dispersion process in particulate porous media at low saturation levels takes place over the surface elements of constituent particles and, as we have found previously by comparison with experiments, can be accurately described by…

Soft Condensed Matter · Physics 2019-06-10 Penpark Sirimark , Alex V. Lukyanov , Tristan Pryer

We consider the spectral structure of indefinite second order boundary-value problems on graphs. A variational formulation for such boundary-value problems on graphs is given and we obtain both full and half-range completeness results. This…

Spectral Theory · Mathematics 2017-07-05 Sonja Currie , Bruce Alastair Watson

Let P^n denote the n-dimensional projective space defined over the algebraic closure of a finite field F_q, let V contained P^n be a complete intersection defined over F_q of dimension r and singular locus of dimension at most s, and let…

Algebraic Geometry · Mathematics 2013-06-06 Antonio Cafure , Guillermo Matera , Melina Privitelli

Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.

Numerical Analysis · Mathematics 2022-09-01 Qusay Muzaffar , Nira Dyn , David Levin

In the present paper, we study problems related to the classical Borsuk's problem. Recall that the Borsuk's problem consists in finding the smallest number $ f(n) $ of parts of smaller diameter into which an arbitrary set of diameter 1 in…

Combinatorics · Mathematics 2025-08-21 Arthur Igorevich Bikeev , Andrei Mikhailovich Raigorodskii

A numerical scheme is described for accurately accommodating oblique, non-aligned, boundaries, on a three-dimensional cartesian grid. The scheme gives second-order accuracy in the solution for potential of Poisson's equation using compact…

Computational Physics · Physics 2011-05-09 Ian H Hutchinson

The finite spectrum of a first-order sentence is the set of positive integers that are the sizes of its models. The class of finite spectra is known to be the same as the complexity class NE. We consider the spectra obtained by limiting…

Logic in Computer Science · Computer Science 2023-06-22 Anuj Dawar , Eryk Kopczyński

It will be shown that every N-graded Lie algebra generated in degree 1 of type FP with entropy less or equal to 1 must be finite-dimensional (cf. Thm. A). As a consequence every Koszul Lie algebra with entropy less or equal to 1 must be…

Rings and Algebras · Mathematics 2013-05-28 Thomas Weigel

We establish a Fatou-type Theorem for $J$-holomorphic mappings that are bounded in an appropriate sense and we prove the Blaschke condition for their zero sets. We also prove a Privalov-type uniqueness Theorem for pairs of $J$-holomorphic…

Complex Variables · Mathematics 2009-03-02 S. Ivashkovich , J. -P. Rosay

We are interested to bound from below the number of distinct dot products determined by a finite set of points $P$ in the Euclidean plane. In this paper, we build on the work of B. Hanson, O. Roche-Newton, and S. Senger, to obtain the…

Combinatorics · Mathematics 2025-02-19 Michalis Kokkinos

In this thesis, we present various contributions to the study of free boundary minimal surfaces. After introducing some basic tools and discussing some delicate aspects related to the definition of Morse index when allowing for a contact…

Differential Geometry · Mathematics 2022-08-26 Giada Franz

Computing accurate splines of degree greater than three is still a challenging task in today's applications. In this type of interpolation, high-order derivatives are needed on the given mesh. As these derivatives are rarely known and are…

Numerical Analysis · Mathematics 2023-03-20 A. Pepin , S. Léger , N. Beaudoin

We study the Fourier series of circle homeomorphisms and circle embeddings, with the emphasis on Blaschke product approximation and the vanishing of Fourier coefficients. The analytic properties of the Fourier series are related to the…

Complex Variables · Mathematics 2019-06-05 Leonid V. Kovalev , Xuerui Yang

Let f(x) = f(x_1, ..., x_n) = \sum_{|S| <= k} a_S \prod_{i \in S} x_i be an n-variate real multilinear polynomial of degree at most k, where S \subseteq [n] = {1, 2, ..., n}. For its "one-block decoupled" version, f~(y,z) = \sum_{|S| <= k}…

Discrete Mathematics · Computer Science 2015-12-08 Ryan O'Donnell , Yu Zhao