A. Smirnov

activity

20002026

most citedOn topological tensor products of functional Frechet and DF spaces

10 citations · 49 across the 20 of their papers we have counts for

collaborators

21 papers

math.FA2026

Measure theory without infinities

A. G. Smirnov, M. S. Smirnov

The aim of this paper is to develop a framework for measure theory that avoids infinities and allows for the uniform treatment of positive and vector measures. Our approach is base…

math.FA2022

Completion procedures in measure theory

A. G. Smirnov, M. S. Smirnov

We propose a unified treatment of extensions of group-valued contents (i.e., additive set functions defined on a ring) by means of adding new null sets. Our approach is based on th…

math-ph2020

Coupling constant dependence for the Schrödinger equation with an inverse-square potential

A. G. Smirnov

We consider the one-dimensional Schrödinger equation $- f^{''} + q_{α} f = E f$ on the positive half-axis with the potential $q_{α} (r) = (α - 1/4) r^{- 2}$ . It is known that the value $α = 0$ plays a…

math.CA2017★ 3 cited

A Gronwall-type Trigonometric Inequality

A. G. Smirnov

We prove that the absolute value of the $n$ th derivative of $cos (x)$ does not exceed $n! / (2 n)!$ for all $x > 0$ and $n = 0, 1, \dots$ and obtain a natural generalization of th…

math-ph2015★ 4 cited

Eigenfunction expansions for the Schrödinger equation with inverse-square potential

A. G. Smirnov

We consider the one-dimensional Schrödinger equation $- f " + q_{κ} f = E f$ on the positive half-axis with the potential $q_{κ} (r) = (κ^{2} - 1/4) r^{- 2}$ . For each complex number $ϑ$ , we…

math-ph2014★ 3 cited

Reduction by symmetries in singular quantum-mechanical problems: general scheme and application to Aharonov-Bohm model

A. G. Smirnov

We develop a general technique for finding self-adjoint extensions of a symmetric operator that respect a given set of its symmetries. Problems of this type naturally arise when co…