相关论文: On coupled systems of Kolmogorov equations with ap…

In this paper we prove a Wiener-type characterization of boundary regularity, in the spirit of a classical result by Landis, for a class of evolutive H\"ormander operators. We actually show the validity of our criterion for a larger class…

We study certain dynamical systems which leave invariant an indefinite quadratic form via semigroups or evolution families of complex symmetric Hilbert space operators. In the setting of bounded operators we show that a…

Let a family of gradient Gaussian vector fields on $ \mathbb{Z}^d $ be given. We show the existence of a uniform finite range decomposition of the corresponding covariance operators, that is, the covariance operator can be written as a sum…

Two essential quantities for the analysis of approximation schemes of evolution equations are stability and convergence. We derive stability and convergence of fully discrete approximation schemes of solutions to linear parabolic evolution…

In this work, the existence of solutions (in a suitable sense) to a family of inclusion systems involving fractional, possibly competing, elliptic operators, fractional convection, and homogeneous Dirichlet boundary conditions is…

Calder\'on-Zygmund decompositions of functions have been used to prove weak-type (1,1) boundedness of singular integral operators. In many examples, the decomposition is done with respect to a family of balls that corresponds to some family…

We prove a regularity result for Green's functions that are associated to elliptic second order divergence-type linear PDO's with coefficients in C^{1,\alpha}(\bar{\Omega}). Here \alpha\in (0,1) and \Omega\subset \R^n is a bounded…

In the setting of homogeneous spaces (X,d,{\mu}), it is shown that the commutator of Calder\'on- Zygmund type operators as well as commutator of potential operator with BMO function are bounded in generalized Grand Morrey space. Interior…

For any non-Archimedean local field $\mathbb{K}$ and any integer $n \geq 1$, we show that the Taibleson operator admits a bounded $\mathrm{H}^\infty(\Sigma_\theta)$ functional calculus on the Bochner space $\mathrm{L}^p(\mathbb{K}^n,Y)$ for…

For a given second-order linear elliptic operator $L$ which admits a positive minimal Green function, and a given positive weight function $W$, we introduce a family of weighted Lebesgue spaces $L^p(\phi_p)$ with their dual spaces, where…

Let $E$ and $F$ be Hilbert $C^*$-modules over a $C^*$-algebra $\CAlg{A}$. New classes of (possibly unbounded) operators $t:E\to F$ are introduced and investigated. Instead of the density of the domain $\Def(t)$ we only assume that $t$ is…

A family of systems related to a linear and bilinear evolution of roots of polynomials in the complex plane is considered. Restricted to the line, the evolution induces dynamics of the Coulomb charges in external potentials, while its fixed…

Consider the following Kolmogorov type hypoelliptic operator $$ \mathscr L_t:=\mbox{$\sum_{j=2}^n$}x_j\cdot\nabla_{x_{j-1}}+{\rm Tr} (a_t \cdot\nabla^2_{x_n}), $$ where $n\geq 2$, $x=(x_1,\cdots,x_n)\in(\mathbb R^d)^n =\mathbb R^{nd}$ and…

Harmonic functions $u:{\mathbb R}^n \to {\mathbb R}^m$ are equivalent to integral manifolds of an exterior differential system with independence condition $(M,{\mathcal I},\omega)$. To this system one associates the space of conservation…

We consider nonautonomous semilinear evolution equations of the form \label{semilineq} \frac{dx}{dt}= A(t)x+f(t,x). Here $A(t)$ is a (possibly unbounded) linear operator acting on a real or complex Banach space $\X$ and $f: \R\times\X\to\X$…

We consider a one-parameter family of degenerately elliptic operators $\cal{L}_\gamma$ on the closed disk $\mathbb{D}$, of Keldysh (or Kimura) type, which appears in prior work [Mishra et al., Inverse Problems (2022)] by the authors and…

We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers. Our main findings are that the essential…

Considering evolutionary equations in the sense of Picard, we identify a certain topology for material laws rendering the solution operator continuous if considered as a mapping from the material laws into the set of bounded linear…

The main result of this paper is a proof of the continuity of a family of integral functionals defined on the space of functions of bounded variation with respect to a topology under which smooth functions are dense. These functionals occur…

Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…