Results 51 to 60 of about 6,490,162 (222)

Extremal holomorphic maps and the symmetrised bidisc

, 2012
We introduce the class of $n$-extremal holomorphic maps, a class that generalises both finite Blaschke products and complex geodesics, and apply the notion to the finite interpolation problem for analytic functions from the open unit disc into the ...
Agler, Jim, Lykova, Zinaida A., Young, N. J.   +2 more
core   +2 more sources

Interpolation and random interpolation in de Branges–Rovnyak spaces

Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.
Abstract The aim of this paper is to characterize universal and multiplier interpolating sequences for de Branges–Rovnyak spaces H(b)$\mathcal {H}(b)$ where the defining function b$b$ is a general non‐extreme rational function. Our results carry over to recently introduced higher order local Dirichlet spaces and thus generalize previously known results
Andreas Hartmann, Giuseppe Lamberti
wiley   +1 more source

Entire and meromorphic solutions for systems of the differential difference equations

Demonstratio Mathematica, 2022
With the help of the Nevanlinna theory of meromorphic functions, the purpose of this article is to describe the existence and the forms of transcendental entire and meromorphic solutions for several systems of the quadratic trinomial functional equations:
Xu Hong Yan, Li Hong, Ding Xin
doaj   +1 more source

Solutions for Several Quadratic Trinomial Difference Equations and Partial Differential Difference Equations in ${\mathbb{C}}^2$

Axioms, 2021
This article is to investigate the existence of entire solutions of several quadratic trinomial difference equations f(z+c)2+2αf(z)f(z+c)+f(z)2=eg(z), and the partial differential difference equations f(z+c)2+2αf(z+c)∂f(z)∂z1+∂f(z)∂z12=eg(z),f(z+c)2+2αf ...
Hong Li, Hongyan Xu
doaj   +1 more source

Siciak-Zahariuta extremal functions, analytic discs and polynomial hulls

, 2008
We prove two disc formulas for the Siciak-Zahariuta extremal function of an arbitrary open subset of complex affine space. We use these formulas to characterize the polynomial hull of an arbitrary compact subset of complex affine space in terms of ...
E.A. Poletsky, F. Lárusson, F. Lárusson, F. Lárusson, Finnur Lárusson, J.B. Garnett, Ragnar Sigurdsson, S. Momm, S.Q. Bu   +8 more
core   +1 more source

Homozygous FANCM Variant c.5101C>T p.(Gln1701*) in a Patient With Early Onset Breast Cancer, Chemotherapy Toxicity, and Chromosome Fragility: A Case Report

Cancer Reports, Volume 8, Issue 8, August 2025.
ABSTRACT Background Biallelic FANCM variants are linked to a Fanconi anemia‐like cancer predisposition syndrome, which includes early onset breast cancer, chemotherapy toxicity, and chromosome fragility. Additionally, heterozygous truncating variants have been linked to increased breast cancer risk. However, the published results have been inconsistent,
Sonja Sulkava, Anna H. Hakonen, Rikke Christensen, Minna Pöyhönen, Heli Nevanlinna   +4 more
wiley   +1 more source

The Exact Solutions for Several Partial Differential-Difference Equations with Constant Coefficients

Mathematics, 2022
This article is concerned with the description of the entire solutions of several Fermat type partial differential-difference equations (PDDEs) μf(z)+λfz1(z)2+[αf(z+c)−βf(z)]2=1, and μf(z)+λ1fz1(z)+λ2fz2(z)2+[αf(z+c)−βf(z)]2=1, where fz1(z)=∂f∂z1 and fz2(
Hongyan Xu, Ling Xu, Hari Mohan Srivastava   +2 more
doaj   +1 more source

Factorizations induced by complete Nevanlinna-Pick factors

, 2018
We prove a factorization theorem for reproducing kernel Hilbert spaces whose kernel has a normalized complete Nevanlinna-Pick factor. This result relates the functions in the original space to pointwise multipliers determined by the Nevanlinna-Pick ...
Aleman, Alexandru, Hartz, Michael, McCarthy, John E., Richter, Stefan   +3 more
core   +1 more source

Transforming Room Acoustics with Causality‐Driven Dual‐Function Passive Metamaterials

Advanced Materials Technologies, Volume 10, Issue 11, June 5, 2025.
This work presents an dual acoustic metamaterial for rooms that achieves excellent broadband performance for both sound absorption and sound diffusion. This is done by using causality formulations linking the absorption of the passive system to its volume, yielding an optimal surface area ratio required for excellent sound absorption and while ...
Eric Ballestero, Yang Meng, Ping Sheng, Vincent Tournat, Vicent Romero‐García, Jean‐Philippe Groby   +5 more
wiley   +1 more source

Some unity results on entire functions and their difference operators related to 4 CM theorem

Journal of Inequalities and Applications, 2020
This paper is to consider the unity results on entire functions sharing two values with their difference operators and to prove some results related to 4 CM theorem. The main result reads as follows: Let f ( z ) $f(z)$ be a nonconstant entire function of
BaoQin Chen, Sheng Li
doaj   +1 more source