arXiv subjects

Sergey Lvin

Publications and source records attributed to Sergey Lvin.

2 recordsLinked to original sources

arXiv2018

Some binomial formulas for non-commuting operators

Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second commutator $[D,[D,U]]$ is proportional to $U$. Operators $D=d/dx$ (differentiation) and $U$- multiplication by $e^{λx}$ or by $\sin λx$ are basic examples, for which some of these relations appeared unexpectedly as byproducts of an authors' previous medical imaging research.

math.CA↗

arXiv2011

Identities for sin(x) that came from medical imaging

The article describes interesting nonlinear differential identities satisfied by standard exponential and trigonometric functions, which appeared as byproducts of medical imaging research. They look like some kind of non-commutative binomial formulas. A brief description of the origin of these identities is provided, as well as their direct algebraic derivation. Relations with separate analyticity theorems in several complex variables and some open problems are also mentioned.

math.CA↗