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Preprint Oct 2026

Gaussian Exterior Dilation and Schatten Classes of L\'evy Area

We study the skew-adjoint Hilbert--Schmidt operator obtained by evaluating a fixed Hilbert two-form on a centered Gaussian linear map whose covariance is the inner product on its domain multiplied by a fixed nonnegative trace-class operator. We compute the expected regularized determinant of the resulting random operat...

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Preprint Sep 2026

Sharp spectral-scale stability for parabolic equations with measure-valued delay

We study the dependence of parabolic solution operators on a finite signed measure describing the delay law. For a positive self-adjoint generator with compact inverse, a weighted dyadic spectral sum characterizes the norm of the semigroup-integrated memory perturbation. An exact realization identity transfers the matc...

Lennon Jason Shikhman · 1 citation · ⚡1
Preprint Sep 2026

Exact Traces for Vector-Valued Morrey Spaces

Trace spaces determine exactly which initial values are compatible with an evolution class. We identify the exact trace generated by vector-valued Morrey control in time and show that it differs essentially from the classical $L^p$ theory. For a Banach couple $X_1\hookrightarrow X_0$, the trace of the natural Morrey ev...

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Preprint Sep 2026

Quantitative homogenization and large-scale regularity for nondivergence-form equations under a critical ellipticity moment

We prove quantitative homogenization estimates for linear elliptic equations in nondivergence form with stationary, symmetric coefficients, finite range of dependence, and a deterministic upper ellipticity bound. No deterministic positive lower bound is imposed. We assume that the reciprocal of the infimum of the small...

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Preprint Oct 2026

Universal operators: topology and consequences of ISP failure

Assuming a negative answer to the invariant subspace problem for separable complex Hilbert spaces, we prove that every universal operator has a continuum of minimal infinite-dimensional invariant subspaces with pairwise trivial intersections. These subspaces can be chosen so that the restrictions are invertible and the...

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Preprint Oct 2026

Exact lattice resonances and a sharp second Picard obstruction for the two-dimensional inviscid primitive equations

We study periodic perturbations of a rest state with constant stable stratification for the two-dimensional non-rotating primitive equations without viscosity or thermal diffusion on a fixed rectangular torus. Fourier resonance analysis and Sobolev estimates show that, despite unitary linear evolution, the polarized se...

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