Search · four archives
Search · four archives
17 papers · ranked by Valyu relevance
André Rosenbaum Coelho, Caio Simon de Oliveira, Sinai Robins
We study the action of the Hecke operators Un on the space R of rational functions in one variable, over C. The main goal is to give a complete classification of the eigenfunctions of Un. We accomplish this by introducing certain number-theoretic directed graphs, called Zolotarev Graphs, which extend the well-known…
Mainak Bhowmik, Mihai Putinar
We return to Takagi's variational principle, generalized after forty years to two complex variables by Pfister. Both isolating some extremal rational functions associated to a bounded holomorphic function in the unit disk, respectively the bidisk. The rational inner functions arising from the Takagi-Pfister skew…
Michael T. Jury, Robert T. W. Martin, Eli Shamovich
A rational function belongs to the Hardy space, H2 , of square-summable power series if and only if it is bounded in the complex unit disk. Any such rational function is necessarily analytic in a disk of radius greater than one. The inner-outer factorization of a rational function, r ∈ H2 is particularly simple: The…
Claire Burrin, Uri Shapira, Shucheng Yu
We study the limiting distribution of the rational points under a horizontal translation along a sequence of expanding closed horocycles on the modular surface. Using spectral methods we confirm equidistribution of these sample points for any translate when the sequence of horocycles expands within a certain polynomial…
Nujood M. Alshehri, Zinaida A. Lykova
In this paper, we prove a Schwarz lemma for the pentablock. The pentablock $\mathcal{P}$ is defined by \begin{aligned}\mathcal{P}={a_{21},{\text{tr}}A, \det A : A=[a_{ij}]_{i,j=1}^2 \in \mathbb{B}^{2\times 2}}\end{aligned} where $\mathbb{B}^{2\times 2}$ denotes the open unit ball in the space of $2\times 2$ complex…
Joseph A. Ball, Dmitry S. Kaliuzhnyi-Verbovetskyi
The Bessmertny˘ı class consists of rational matrix-valued functions of d complex variables representable as the Schur complement of a block of a linear pencil A(z) = z1A1 + · · · + zdAd whose coefficients Ak are positive semidefinite matrices. We show that it coincides with the subclass of rational functions in the…
Zijia Li, Ke Ye
This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify quadratic rational curves on Un, On(R), On−1,1(R) and On−2,2(R). (ii) We prove a…
Jurij Volčič
This paper solves the rational noncommutative analog of Hilbert's 17th problem: if a noncommutative rational function is positive semidefinite on all tuples of hermitian matrices in its domain, then it is a sum of hermitian squares of noncommutative rational functions. This result is a generalization and culmination of…
Sigmundur Gudmundsson, Adam Lindström
In this work we find a unifying scheme for the known explicit complex-valued eigenfunctions on the classical compact Riemannian symmetric spaces. For this we employ the well-known Cartan embedding for those spaces. This also leads to the construction of new eigenfunctions on the quaternionic Grassmannians.
Matthew S. Schmitt, Maciej Koch-Janusz, Michel Fruchart, Daniel S. Seara + 2 more
Model reduction is the construction of simple yet predictive descriptions of the dynamics of many-body systems in terms of a few relevant variables. A prerequisite to model reduction is the identification of these relevant variables, a task for which no general method exists. Here, we develop a systematic approach…
Doyon Kim
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\operatorname {GL}(r,{\mathbb {R}})$$\end{document} GL ( r , R ) part I: Combinatorics Authors: Doyon Kim We give a…
Adam Lindström
Symmetric Spaces via the Cartan Embedding Authors: ['Adam Lindström'] Given a symmetric triple (G, K, σ) of compact type, with Gσ = K, the well known Cartan embedding Φ : ˆ G/K → G homothetically embeds the symmetric space M = G/K as a totally geodesic submanifold of G. In this thesis we show that Φ and the related ˆ…
Bingjie Wu, James Holehouse, Ramon Grima, Chen Jia
In this study, we obtain an exact time-dependent solution of the chemical master equation (CME) of an extension of the two-state telegraph model describing bursty or non-bursty protein expression in the presence of positive or negative autoregulation. Using the method of spectral decomposition, we show that the…
Keisuke Fujii, Naoya Takeishi, Benio Kibushi, Motoki Kouzaki + 1 more
Living organisms dynamically and flexibly operate a great number of components. As one of such redundant control mechanisms, low-dimensional coordinative structures among multiple components have been investigated. However, structures extracted from the conventional statistical dimensionality reduction methods do not…
Sucheta Ghosh, Shankar Prasad Bhattacharyya
The quantum states of hydrogen atom in one dimension can be obtained by a careful application of the well-known Frobenius method. The exercise is highly educative and brings to focus the subtle aspects of quantum mechanics. The allowed states turn out to be only of odd parity and non-degenerate, having energy given by…
Sylvain Carpentier, Alexander V. Mikhailov, Jing Ping Wang
In this paper we introduce the concept of preHamiltonian pairs of difference operators, demonstrate their connections with Nijenhuis operators and give a criteria for the existence of weakly nonlocal inverse recursion operators for differential-difference equations. We begin with a rigorous setup of the problem in…
Authors not listed
In these Notes we present a new perspective on the exact-factorization expression of a molecular wavefunction, which does not rely of the probabilistic interpretation of the molecular wavefunction as a joint probability amplitude. Instead, we demonstrate a close relation with the traditional Born-Huang representation…