arXiv subjects

Andrey Russanov

Publications and source records attributed to Andrey Russanov.

2 recordsLinked to original sources

arXiv2026

Log-Sobolev and Beckner inequalities and stability of Poincaré inequality with weighted Gaussian measures

We employ a Markov semigroup approach combined with the $Γ$-calculus to establish a generalized Beckner inequality associated with weighted Gaussian measures. As a direct consequence, we derive the corresponding Poincaré inequality in the same setting. Subsequently, by means of a duality argument, we investigate gradient and $L^2$ stability estimates of the Poincaré inequality. Furthermore, we formulate a scale-dependent version of the Poincaré inequality for homogeneous Gaussian-type measures and apply it to analyze the stability of the Heisenberg Uncertainty Principle with homogeneous weights. Finally, we establish a Logarithmic Sobolev inequality for weighted Gaussian measures and utilize it to derive the Euclidean Logarithmic Sobolev inequality with homogeneous log-concave weights.

math.FA↗

arXiv2025

Stability of Gaussian Poincaré inequalities and Heisenberg Uncertainty Principle with monimial weights

We use the Bakry-Émery curvature-dimension criterion and $Γ$-calculus to establish the Poincaré inequality with monomial Gaussian measure, and then apply the duality approach to study its improvements and its gradient stability. We also set up the scale-dependent Poincaré inequality with monomial Gaussian type measure and use it to inspect the stability of the Heisenberg Uncertainty Principle with monomial weight. Finally, we apply the improved versions of the monomial Gaussian Poincaré inequality to investigate the improved stability of the Heisenberg Uncertainty Principle with monomial weight. As special cases of our main results, we obtain the gradient stability of the classical Gaussian Poincaré inequality, which is of independent interest. Moreover, we also establish the stability of the sharp stability inequality of the classical Heisenberg Uncertainty Principle proved in [15].

math.AP↗