Related papers: A strong type inequality for convolution with squa…

We consider the torsional rigidity and the principal eigenvalue related to the $p$-Laplace operator. The goal is to find upper and lower bounds to products of suitable powers of the quantities above in various classes of domains. The limit…

We prove a uniform generalized gaussian bound for the powers of a discrete convolution operator in one space dimension. Our bound is derived under the assumption that the Fourier transform of the coefficients of the convolution operator is…

In this paper, we are interested in the behavior of the typical Poisson-Voronoi cell in the plane when the radius of the largest disk centered at the nucleus and contained in the cell goes to infinity. We prove a law of large numbers for…

Let $\mathbb{H}^{n}$ be the Heisenberg group. For $0 \leq \alpha < Q=2n+2$ and $N \in \mathbb{N}$ we consider exponent functions $p(\cdot) : \mathbb{H}^{n} \to (0, +\infty)$, which satisfies H\"older conditions, such that $\frac{Q}{Q+N} <…

The structure of Poisson polynomial algebras of the type obtained as semiclassical limits of quantized coordinate rings is investigated. Sufficient conditions for a rational Poisson action of a torus on such an algebra to leave only…

For a bounded three-dimensional domain with Lipschitz boundary we extend Korn's first inequality to incompatible tensor fields. For compatible tensor fields our estimate reduces to a non-standard variant of the well known Korn's first…

For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators,…

In this paper we consider several problems of joint similarity to tuples of bounded linear operators in noncommutative polydomains and varieties associated with sets of noncommutative polynomials. We obtain analogues of classical results…

Kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same…

We consider parabolic operators of the form $$\partial_t+\mathcal{L},\ \mathcal{L}:=-\mbox{div}\, A(X,t)\nabla,$$ in $\mathbb R_+^{n+2}:=\{(X,t)=(x,x_{n+1},t)\in \mathbb R^{n}\times \mathbb R\times \mathbb R:\ x_{n+1}>0\}$, $n\geq 1$. We…

Two degenerate Poisson structures of the same rank possess a recursion operator if and only if their characteristic distributions coincide.

High-precision knowledge of electromagnetic form factors of nuclei is a subject of much current experimental and theoretical activity in nuclear and atomic physics. Such precision mandates that effects of the non-zero spatial extent of the…

This paper is devoted to establishing the kernel theorems for $\alpha$-modulation spaces in terms of boundedness and compactness. We characterize the boundedness of a linear operator $A$ from an $\alpha$-modulation space…

In this work we obtain sharp embedding inequalities for a family of conformally invariant integral extension operators. This family includes among others the classical Poisson extension operator and the extension operator with Riesz kernel.…

We prove optimal H\"older boundary regularity for a non-local operator with a singular, symmetric kernel that depends on the distance to the boundary of the underlying domain. Additionally, we prove higher boundary regularity of solutions.

We extend Stein's maximal theorem to the bilinear setting. Let $M$ be a homogeneous space with a transitive action of a compact abelian group, and let $1 \le p,q \le 2$ and $1/2 \le r \le 1$ satisfy $1/p + 1/q = 1/r$. For a family of…

We prove that the class of convolution-type kernels satisfying suitable decay conditions of the Fourier transform, appearing in the works of Christ, Christ-Rubio de Francia, and Duoandikoetxea-Rubio de Francia gives rise to maximally…

The paper deals with homogenization problem for a non-local linear operator with a kernel of convolution type in a medium with a periodic structure. We consider the natural diffusive scaling of this operator and study the limit behaviour of…

We describe and analyze nonlocal integro-differential equations with classical local boundary conditions. The interaction kernel of the nonlocal operator has horizon parameter dependent on position in the domain, and vanishes as the…

In this paper we analyze the convergence of the following type of series $$ T_N^\alpha f(x,t)=\sum_{j=N_1}^{N_2} v_j(P_{a_{j+1}}^\alpha f(x,t)-P_{a_j}^\alpha f(x,t)),\quad (x,t)\in \mathbb R^{n+1}, \ N=(N_1, N_2)\in \mathbb Z^2,\ \alpha>0,…