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Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory
In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and
operator theory. We first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the
Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. We propose a new notion of tensored-scalar singularity, and
then answer questions on Hankel operators with matrix-valued bounded type symbols. We also examine an interpolation problem related to a
certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejér
Interpolation Problem for matrix rational functions. We then extend the
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The Mother Body Phase Transition in the Normal Matrix Model
The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to
several other topics as quadrature domains, inverse potential problems and the Laplacian growth.
In this present paper we
consider the normal matrix model with cubic plus linear potential. In order to regularize the model, we follow Elbau & Felder and
introduce a cut-off. In the large size limit, the eigenvalues of the model accumulate uniformly within a certain domain
We also study in detail the mother body problem associated to
To construct the mother body measure, we define a quadratic differential
Following previous works of Bleher & Kuijlaars
and Kuijlaars & López, we consider multiple orthogonal polynomials associated with the normal matrix model. Applying the Deift-Zhou
nonlinear steepest descent method to the associated Riemann-Hilbert problem, we obtain strong asymptotic formulas for these polynomials.
Due to the presence of the linear term in the potential, there are no rotational symmetries in the model. This makes the construction of
the associated
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Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume
We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We
then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of
eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume
and the dynamics of their geodesic flows.
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On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function
We present several formulae for the large
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Subset currents on surfaces
Subset currents on hyperbolic groups were introduced by Kapovich and Nagnibeda as a generalization of geodesic currents on hyperbolic
groups, which were introduced by Bonahon and have been successfully studied in the case of the fundamental group
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Recent trends in formal and analytic solutions of diff. equations : Virtual Conference Formal and Analytic Solutions of Diff. Equations, June 28-July 2, 2021, University of Alcalá, Alcalá de Henares, Spain
This volume contains the proceedings of the conference on Formal and Analytic Solutions of Diff. Equations, held from June 28-July 2, 2021, and hosted by University of Alcala, Alcala de Henares, Spain. The manuscripts cover recent advances in the study of formal and analytic solutions of different kinds of equations such as ordinary differential equations, difference equations, $q$-difference equations, partial differential equations, moment differential equations, etc. Also discussed are related topics such as summability of formal solutions and the asymptotic study of their solutions. The volume is intended not only for researchers in this field of knowledge but also for students who aim to acquire new techniques and learn recent results.
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Topics in several complex variables : first USA-Uzbekistan conference analysis and mathematical physics, May 20-23, 2014, California State University, Fullerton, CA
This volume contains the proceedings of the Special Session on Several Complex Variables, which was held during the first USA-Uzbekistan Conference on Analysis and Mathematical Physics from May 20-23, 2014, at California State University, Fullerton.This volume covers a wide variety of topics in pluripotential theory, symplectic geometry and almost complex structures, integral formulas, holomorphic extension, and complex dynamics. In particular, the reader will find articles on Lagrangian submanifolds and rational convexity, multidimensional residues, S-parabolic Stein manifolds, Segre varieties, and the theory of quasianalytic functions.
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Conformal Graph Directed Markov Systems on Carnot Groups
We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped
with a sub-Riemannian metric. In particular, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit
set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen’s parameter. We illustrate our results for a variety of examples
of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include
the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the
non-real classical rank one hyperbolic spaces.
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Differential Equations, Mathematical Physics, and Applications
This is the second of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 733.Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union.The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in ordinary and partial differential equations, fluid dynamics, and various applications.
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