58 citations · 133 across the 18 of their papers we have counts for
20 papers
When does a derivation of a ring admit the exponential?
Genrich Belitskii, Alberto F. Boix, Dmitry Kerner
Exponentials of (real/complex) vector fields are classically defined via the vector field integration. Take a k-algebra k[x] \subset R\subset k[[x]], where k\supseteq \Q is a local…
Congruence of matrix spaces, matrix tuples, and multilinear maps
Genrich R. Belitskii, Vyacheslav Futorny, Mikhail Muzychuk +1
Two matrix vector spaces are said to be equivalent if for some nonsingular and . These spaces are congruent if . We prove t…
New Method of Smooth Extension of Local Maps on Linear Topological Spaces. Applications and Examples
Genrich Belitskii, Victoria Rayskin
The question of extension of locally defined maps to the entire space arises in many problems of analysis (e.g., local linearization of functional equations). A known classical met…
Surjectivity of the completion map for rings of -functions. (Whitney extension theorem for general filtrations)
Genrich Belitskii, Dmitry Kerner
The classical lemma of Borel reads: any power series with real coefficients is the Taylor series of a smooth function. Algebraically this means the surjectivity of the completion m…
Approximation results of Artin-Tougeron-type for general filtrations and for -equations
Genrich Belitskii, Alberto F. Boix, Dmitry Kerner
Artin approximation and other related approximation results are used in various areas. The traditional formulation of such results is restricted to filtrations by powers of ideals,…
Extension of differentiable local mappings on linear topological spaces
Genrich Belitskii, Victoria Rayskin
Usually, for extension of local maps, one uses multiplication by so called bump functions. However, majority of infinite-dimensional linear topological spaces do not have smooth bu…