Related papers: Regular subspaces of symmetric stable processes

In the present paper, we introduce so-called operator-stable-like processes. Roughly speaking, they behave locally like operator-stable processes, but they need not to be homogenous in space. Having shown existence for this class of…

We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. Many of the presented…

It was shown by G. Pisier that any finite-dimensional normed space admits an $\alpha$-regular $M$-position, guaranteeing not only regular entropy estimates but moreover regular estimates on the diameters of minimal sections of its unit-ball…

We discuss random interpolation in weighted Dirichlet spaces $\mathcal{D}_\alpha$, $0\leq \alpha\leq 1$. While conditions for deterministic interpolation in these spaces depend on capacities which are very hard to estimate in general, we…

We introduce and study some generalizations of regular spaces, which were motivated by studying continuity properties of functions between (regular) topological spaces. In particular, we prove that a first-countable Hausdorff topological…

Any symmetric closed subset of a finite crystallographic root system must be a closed subroot system. This is not, in general, true for real affine root systems. In this paper, we determine when this is true and also give a very explicit…

We expose different methods of regularizations of subsolutions in the context of discrete weak KAM theory. They allow to prove the existence and the density of $C^{1,1}$ subsolutions. Moreover, these subsolutions can be made strict and…

If $E=\{e_i\}$ and $F=\{f_i\}$ are two 1-unconditional basic sequences in $L_1$ with $E$ $r$-concave and $F$ $p$-convex, for some $1\le r<p\le 2$, then the space of matrices $\{a_{i,j}\}$ with norm $\|\{a_{i,j}\}\|_{E(F)}=\big\|\sum_k…

For $M$ being a closed manifold or the Euclidean space we present a detailed proof of regularity properties of the composition of $H^s$-regular diffeomorphisms of $M$ for $s > 1/2\dim M + 1$.

Using complex analysis techniques we obtain precise asymptotic approximations for the kernels corresponding to the symmetric $\alpha$-stable processes and their fractional derivatives. We apply our method to general L\'evy processes whose…

For $0<\alpha\le 1$, we say that a sequence $(X_k)_{k>0}$ of $d$-regular graphs has property $D_\alpha$ if there exists a constant $C>0$ such that $\mathrm{diam}(X_k)\ge C\cdot|X_k|^\alpha$. We investigate property $D_\alpha$ for arithmetic…

For $\alpha\in (1,2)$, we present a generalized central limit theorem for $\alpha$-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential…

Given a strongly local Dirichlet space and $\lambda\geq 0$, we introduce a new notion of $\lambda$--subharmonicity for $L^1_\loc$--functions, which we call \emph{local $\lambda$--shift defectivity}, and which turns out to be equivalent to…

In this paper we study the weak convergence of self-normalized partial sum processes in the Skorokhod M1 topology for sequences of random variables which exhibit clustering of large values of the same sign. We show that for stationary…

The Sobolev regularity of invariant measures for diffusion processes is proved on non-smooth metric measure spaces with synthetic lower Ricci curvature bounds. As an application, the symmetrizability of semigroups is characterized, and the…

In this paper, we introduce stable recursive subhomogeneous algebras (SRSHAs), which is analogous to recursive subhomogeneous algebras (RSHAs) introduced by N. C. Phillips in the studies of free minimal integer actions on compact metric…

The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index $\alpha$ ($0< \alpha \le 2$), in the symmetric case. We show that by properly scaled transition to…

We consider the 1-harmonic flow of maps from a bounded domain into a submanifold of a Euclidean space, i.e. the gradient flow of the total variation functional restricted to maps taking values in the manifold. We restrict ourselves to…

Let V be a vector space of dimension n over the finite field F_q, where q is odd, and let Symm(V) denote the space of symmetric bilinear forms defined on V x V. We investigate constant rank r subspaces of Symm(V) in this paper. We have…