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This volume contains the proceedings of the Conference on Complex Analysis and Spectral Theory, in celebration of Thomas Ransford's 60th birthday, held from May 21-25, 2018, at Laval University, Québec, Canada. Spectral theory is the branch of mathematics devoted to the study of matrices and their eigenvalues, as well as their infinite-dimensional counterparts, linear operators and their spectra. Spectral theory is ubiquitous in science and engineering because so many physical phenomena, being essentially linear in nature, can be modelled using linear operators. On the other hand, complex analysis is the calculus of functions of a complex variable. They are widely used in mathematics, physics, and in engineering. Both topics are related to numerous other domains in mathematics as well as other branches of science and engineering. The list includes, but is not restricted to, analytical mechanics, physics, astronomy (celestial mechanics), geology (weather modeling), chemistry (reaction rates), biology, population modeling, economics (stock trends, interest rates and the market equilibrium price changes). There are many other connections, and in recent years there has been a tremendous amount of work on reproducing kernel Hilbert spaces of analytic functions, on the operators acting on them, as well as on applications in physics and engineering, which arise from pure topics like interpolation and sampling. Many of these connections are discussed in articles included in this book.

Wilhelm Magnus was an extraordinarily creative mathematician who made fundamental contributions to diverse areas, including group theory, geometry, and special functions. This book contains the proceedings of a conference held in May 1992 at Polytechnic University to honor the memory of Magnus. The focus of the book is on active areas of current research where Magnus' influence can be seen. The papers range from expository articles to major new research, bringing together seemingly diverse topics and providing entry points to a variety of areas of mathematics.

This book presents a collection of papers on certain aspects of general operator theory related to classes of important operators: singular integral, Toeplitz and Bergman operators, convolution operators on Lie groups, pseudodifferential operators, etc. The study of these operators arises from integral representations for different classes of functions, enriches pure operator theory, and is influential and beneficial for important areas of analysis.Particular attention is paid to the fruitful interplay of recent developments of complex and hypercomplex analysis on one side and to operator theory on the other. The majority of papers illustrate this interplay as well as related applications. The papers represent the proceedings of the conference \"\"Operator Theory for Complex and Hypercomplex Analysis\"\", held in December 1994 in Mexico City.

This volume contains the proceedings of the Seventh International Conference on Complex Analysis and Dynamical Systems, held from May 10-15, 2015, in Nahariya, Israel. The papers in this volume range over a wide variety of topics in the interaction between various branches of mathematical analysis. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, geometry, harmonic analysis, and partial differential equations, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis.

This volume contains the proceedings of the 11th International Symposium on Orthogonal Polynomials, Special Functions, and their Applications, held August 29-September 2, 2011, at the Universidad Carlos III de Madrid in Leganes, Spain. The papers cover asymptotic properties of polynomials on curves of the complex plane, universality behavior of sequences of orthogonal polynomials for large classes of measures and its application in random matrix theory, the Riemann-Hilbert approach in the study of Pade approximation and asymptotics of orthogonal polynomials, quantum walks and CMV matrices, spectral modifications of linear functionals and their effect on the associated orthogonal polynomials, bivariate orthogonal polynomials, and optimal Riesz and logarithmic energy distribution of points. The methods used include potential theory, boundary values of analytic functions, Riemann-Hilbert analysis, and the steepest descent method.

This valuable collection of articles presents the latest methods and results in complex analysis and its applications. The present trends in complex analysis reflected in the book are concentrated in the following research directions: Clifford analysis, complex dynamical systems, complex function spaces, complex numerical analysis, qusiconformal mapping, Riemann surfaces, Teichmüller theory and Klainian groups, several complex variables, and value distribution theory.Sample Chapter(s)Chapter 1: Complex Boundary Value Problems in a Quarter Plane (490 KB)Contents:Complex Boundary Value Problems in a Quarter Plane (H Begehr & G Harutyunyan)A Change of Scale Formula for Wiener Integrals of Unbounded Functions over Wiener Paths in Abstract Wiener Space (K S Chang et al.)Qp-Spaces: Generalizations to Bounded Symmetric Domains (M Engliš)Order of Growth of Painlevé Transcendents (A Hinkkanen & I Laine)A Remark on Holomorphic Sections of Certain Holomorphic Families of Riemann Surfaces (Y Imayoshi & T Nogi)α-Asymptotically Conformal Fixed Points and Holomorphic Motions (Y Jiang)Uniqueness Theory of Meromorphic Functions in an Angular Domain (W Lin & S Mori)On Nevanlinna Type Classes (N Sukantamala & Z Wu)On Non-Existence of Teichmüller Extremal (G Yao)The Möbius Invariance of Besov Spaces on the Unit Ball of Xn (K Zhu)and other papersReadership: Researchers and graduates in complex analysis.