» Mixing Properties of Stable Random Fields Indexed by Amenable and Hyperbolic Groups. (arXiv:2205.15849v2 [math.PR] UPDATED)
04/07/22 10:58 from math.OA updates on arXiv.org
We show that any stationary symmteric $\alpha$-stable ($S\alpha S$) random field indexed by a countable amenable group $G$ is weakly mixing if and only if it is generated by a null action, extending works of Samorodnitsky and Wang-Roy-St...

» A Banach space $C(K)$ reading the dimension of $K$. (arXiv:2207.00149v1 [math.FA])
04/07/22 10:58 from math.FA updates on arXiv.org
Assuming Jensen's diamond principle ($\diamondsuit$) we construct for every natural number $n>0$ a compact Hausdorff space $K$ such that whenever the Banach spaces $C(K)$ and $C(L)$ are isomorphic for some compact Hausdorff $L$, then ...

» Stability of the ball for attractive-repulsive energies. (arXiv:2207.00388v1 [math.AP])
04/07/22 10:58 from math.FA updates on arXiv.org
We consider a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. It has recently been proved by R. Frank and E. Lieb that the ball is the un...

» The Cheeger problem in abstract measure spaces. (arXiv:2207.00482v1 [math.MG])
04/07/22 10:58 from math.FA updates on arXiv.org
We consider non-negative $\sigma$-finite measure spaces coupled with a proper functional $P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant...

» A necessary condition for Sobolev extension domains in higher dimensions. (arXiv:2207.00541v1 [math.AP])
04/07/22 10:58 from math.FA updates on arXiv.org
We give a necessary condition for a domain to have a bounded extension operator from $L^{1,p}(\Omega)$ to $L^{1,p}(\mathbb R^n)$ for the range $1 < p < 2$. The condition is given in terms of a power of the distance to the boundary ...

» Geometry of holomorphic vector bundles and similarity of commuting operator tuples. (arXiv:1801.01680v5 [math.FA] UPDATED)
04/07/22 10:58 from math.FA updates on arXiv.org
In this paper, a new criterion for the similarity of commuting tuples of operators on Hilbert spaces is introduced. As an application, we obtain a geometric similarity invariant of tuples in the Cowen-Douglas class which gives a partial ...

» Transport of Gaussian measures with exponential cut-off for Hamiltonian PDEs. (arXiv:2103.04408v3 [math.AP] UPDATED)
04/07/22 10:58 from math.FA updates on arXiv.org
We show that introducing an exponential cut-off on a suitable Sobolev norm facilitates the proof of quasi-invariance of Gaussian measures with respect to Hamiltonian PDE flows and allows us to establish the exact Jacobi formula for the d...

» A second-order Magnus-type integrator for evolution equations with delay. (arXiv:2202.04194v2 [math.NA] UPDATED)
04/07/22 10:58 from math.FA updates on arXiv.org
We rewrite abstract delay equations to nonautonomous abstract Cauchy problems allowing us to introduce a Magnus-type integrator for the former. We prove the second-order convergence of the obtained Magnus-type integrator. We also show th...