The international conference entitled ‘New Trends in Approximation Theory’ was held at the Fields Institute, in Toronto, from July 25 until July 29, 2016. The conference was fondly dedicated to the memory of our unique friend and colleague, André Boivin, who gave tireless service in Canada until his very last moment of his life in October 2014. The impact of his warm personality and his fine work on Complex Approximation Theory was reflected by the mathematical excellence and the wide research range of the 37 participants. In total there were 27 talks, delivered by well-established mathematicians and young researchers. In particular, 19 invited lectures were delivered by leading experts of the field, from 8 different countries.
The wide variety of presentations composed a mosaic of aspects of approximation theory, highlighting interesting connections with important contemporary areas of Analysis. Primary topics discussed include application of approximation theory (isoperimetric inequalities, construction of entire order-isomorphisms, dynamical sampling); approximation by harmonic and holomorphic functions (especially uniform and tangential approximation), polynomial and rational approximation; zeros of approximants and zero-free approximation; tools used in approximation theory; approximation on complex manifolds, in product domains, and in function spaces; and boundary behaviour and universality properties of Taylor and Dirichlet series.
Зміст
Preface.- The life and work of André Boivin (Gauthier, Manolaki, Mashreghi).- A note on the density of rational functions in A¥(W) (Falco, Nestoridis, Zadik).- Approximation by entire functions in the construction of order-isomorphisms and large cross-sections (Burke).- Approximation by solutions of elliptic equations and extension of subharmonic functions (Gauthier, Paramonov).- Approximation in the closed unit ball (Mashreghi, Ransford).- A Thought on Approximation by Bi-Analytic Functions (Khavinson).- Chebyshev polynomials associated with a system of continua (De Frain).- Constrained L2-approximation by polynomials on subsets of the circle (Baratchart, Leblond, Seyfert).- Extremal bounds of Tichmuller-Wittich-Belinskii type for planar quasiregular mappings (Golberg).- Families of Universal Taylor Series depending on a parameter (Abakumov, Muller, Nestoridis).- Interpolation by bounded analytic functions and related questions (Danielyan).- On two interpolation formulasfor complex polynomials (Fournier, Ruscheweyh).- Operators with simple orbital behavior (Prajitura).- Taylor series, universality and potential theory (Gardiner).- Subharmonic images of a convergent sequence (Gauthier, Manolaki).
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