@book{AizenbergTarkhanov2005, author = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich}, title = {Stable expansions in homogeneous polynomials}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {23 S.}, year = {2005}, language = {en} } @unpublished{AizenbergTarkhanov1999, author = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich}, title = {A Bohr phenomenon for elliptic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25547}, year = {1999}, abstract = {In 1914 Bohr proved that there is an r ∈ (0, 1) such that if a power series converges in the unit disk and its sum has modulus less than 1 then, for |z| < r, the sum of absolute values of its terms is again less than 1. Recently analogous results were obtained for functions of several variables. The aim of this paper is to comprehend the theorem of Bohr in the context of solutions to second order elliptic equations meeting the maximum principle.}, language = {en} } @unpublished{AizenbergTarkhanov2005, author = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich}, title = {Stable expansions in homogeneous polynomials}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29925}, year = {2005}, abstract = {An expansion for a class of functions is called stable if the partial sums are bounded uniformly in the class. Stable expansions are of key importance in numerical analysis where functions are given up to certain error. We show that expansions in homogeneous functions are always stable on a small ball around the origin, and evaluate the radius of the largest ball with this property.}, language = {en} } @unpublished{AizenbergTarkhanov2014, author = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich}, title = {An integral formula for the number of lattice points in a domain}, volume = {3}, number = {3}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70453}, pages = {7}, year = {2014}, abstract = {Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of R^n and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain.}, language = {en} } @book{AizenbergTarchanov1999, author = {Aizenberg, Lev A. and Tarchanov, Nikolaj N.}, title = {A Bohr phenomenon for elliptic equations}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {24 S.}, year = {1999}, language = {en} }