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...
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...
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...
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...
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...
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...
Feng-Jie Luo, Zheng-Dong Du· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.