Author

K. Nyström

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Preprint Sep 2026

Weighted Kolmogorov equations: transfer estimates, local boundedness, and Harnack inequalities

Let $m\geq1$, $k\geq0$, $n=m+k$, and write $x=(v,z)\in\mathbb R^m\times \mathbb R^k$, where $v$ is the active velocity variable and $z$ is passive with respect to $Y=v\cdot\nabla_y+\partial_t$. We consider \[ \operatorname{div}_x(A\nabla_xu)-Y(wu)=0, \] where $w=w(x)\in A_2(\mathbb R^n)$ and the measurable matrix $A$ h...

K. Nyström · 0 citations

Preprint Sep 2026

Solvability of the $\mathrm L^2$ Dirichlet problem for parabolic operators with spatially periodic coefficients

We prove global reverse H\"older estimates in $\mathrm L^2$ for the Poisson kernel of scalar divergence-form parabolic operators in the upper half-space. The coefficient matrix is real, symmetric, and periodic in every spatial variable $X=(\lambda,x)$, while no periodicity in time is assumed. If its boundary trace...

K. Nyström · 0 citations

Preprint Aug 2026

A Commutator Framework for Selective Spectral Alignment in Deep Neural Networks

We develop a finite-width geometric framework describing how learned feature geometries are organized, transported, and selectively aligned in deep neural networks. Incompatibility among weight-generated covariance, gates, and backward sensitivities is quantified through three families of commutators: between gates and...

K. Nyström · 0 citations

K. Nyström

Weighted Kolmogorov equations: transfer estimates, local boundedness, and Harnack inequalities

Solvability of the \(\mathrm L^2\) Dirichlet problem for parabolic operators with spatially periodic coefficients

A Commutator Framework for Selective Spectral Alignment in Deep Neural Networks