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"Complex variables"
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Local dynamics of non-invertible maps near normal surface singularities
We study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs
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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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Weighted Bergman spaces induced by rapidly increasing weights
This monograph is devoted to the study of the weighted Bergman space $A^p_\\omega$ of the unit disc $\\mathbb{D}$ that is induced by a radial continuous weight $\\omega$ satisfying $\\lim_{r\\to 1^-}\\frac{\\int_r^1\\omega(s)\\,ds}{\\omega(r)(1-r)}=\\infty.$ Every such $A^p_\\omega$ lies between the Hardy space $H^p$ and every classical weighted Bergman space $A^p_\\alpha$. Even if it is well known that $H^p$ is the limit of $A^p_\\alpha$, as $\\alpha\\to-1$, in many respects, it is shown that $A^p_\\omega$ lies ``closer'' to $H^p$ than any $A^p_\\alpha$, and that several finer function-theoretic properties of $A^p_\\alpha$ do not carry over to $A^p_\\omega$.
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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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New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in ℝⁿ
The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable
conformal minimal surfaces in
All our new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice
of a conformal structure. This enables us to obtain significant new applications to the global theory of non-orientable minimal
surfaces. In particular, we construct proper non-orientable conformal minimal surfaces in
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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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Analysis and geometry in several complex variables : workshop on Analysis and Geometry in Several Complex Variables, January 4-8, 2015, Texas A&M University at Qatar, Doha, Qatar
This volume contains the proceedings of the workshop on Analysis and Geometry in Several Complex Variables, held from January 4-8, 2015, at Texas A&M University at Qatar, Doha, Qatar.This volume covers many topics of current interest in several complex variables, CR geometry, and the related area of overdetermined systems of complex vector fields, as well as emerging trends in these areas.Papers feature original research on diverse topics such as the rigidity of CR mappings, normal forms in CR geometry, the d-bar Neumann operator, asymptotic expansion of the Bergman kernel, and hypoellipticity of complex vector fields. Also included are are two survey articles on complex Brunn-Minkowski theory and the regularity of systems of complex vector fields and their associated Laplacians.
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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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