Tomasz Kania

Parallelepipeds of Maximal Facet Area and Total Edge Length in Ellipsoids, Through Prescribed Boundary Points

Let \[ \mathcal{E}_A=\{x\in\mathbb{R}^n:x^{\top}A^{-1}x\le 1\},\qquad n\ge2, \] where $A$ is real symmetric positive definite. We study full-dimensional parallelepipeds whose $2^n$ vertices lie on $\partial\mathcal{E}_A$. First we show that such parallelepipeds are necessarily ce...

Law Equivalence for Ornstein–Uhlenbeck Dynamics Driven by Lévy Noise

For stochastic partial differential equations driven by Lévy noise, understanding when changes in the drift operator preserve the law of the solution is fundamental to filtering, control, and simulation. We extend law-comparison results for Ornstein–Uhlenbeck processes from bound...

Hamana’s injective envelope as a maximal rigid multiplier cover

Abstract Let A be a unital $$C^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> -algebra. An A -multiplier cover is a $$C^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup>...