@unpublished{ElinShoikhetTarkhanov2015, author = {Elin, Mark and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich}, title = {Analytic semigroups of holomorphic mappings and composition operators}, volume = {4}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77914}, pages = {30}, year = {2015}, abstract = {In this paper we study the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators. We also provide a brief review around this topic.}, language = {en} } @article{ElinShoikhetTarkhanov2017, author = {Elin, Mark and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich}, title = {Analytic Semigroups of Holomorphic Mappings and Composition Operators}, series = {Computational Methods and Function Theory}, volume = {18}, journal = {Computational Methods and Function Theory}, number = {2}, publisher = {Springer}, address = {Heidelberg}, issn = {1617-9447}, doi = {10.1007/s40315-017-0227-x}, pages = {269 -- 294}, year = {2017}, abstract = {In this manuscript we provide a review on the classical and resent results related to the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators.}, language = {en} } @article{ElinShoikhetTarkhanov2011, author = {Elin, Mark and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich}, title = {Separation of boundary singularities for holomorphic generators}, series = {Annali di matematica pura ed applicata}, volume = {190}, journal = {Annali di matematica pura ed applicata}, number = {4}, publisher = {Springer}, address = {Heidelberg}, issn = {0373-3114}, doi = {10.1007/s10231-010-0165-y}, pages = {595 -- 618}, year = {2011}, abstract = {We prove a theorem on separation of boundary null points for generators of continuous semigroups of holomorphic self-mappings of the unit disk in the complex plane. Our construction demonstrates rather strikingly the particular role of the binary operation au broken vertical bar given by 1/ f au broken vertical bar g = 1/f + 1/g on generators.}, language = {en} } @unpublished{GibaliShoikhetTarkhanov2015, author = {Gibali, Aviv and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich}, title = {On the convergence of continuous Newton method}, volume = {4}, number = {10}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-81537}, pages = {15}, year = {2015}, abstract = {In this paper we study the convergence of continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on a recent progress in the geometric theory of spirallike functions. We prove convergence theorems and illustrate them by numerical simulations.}, language = {en} }