Related papers: Regular Dirichlet extensions of one-dimensional Br…
Using the Dirichlet theorem on the equidistribution of residue classes modulo $q$ and the Lemke Oliver-Soundararajan conjecture on the distribution of pairs of residues on consecutive primes, we show that the domain of convergence of the…
Using Girsanov transformations we construct from sticky reflected Brownian motion on $[0,\infty)$ a conservative diffusion on $E:=[0,\infty)^n$, $n \in \mathbb{N}$, and prove that its transition semigroup possesses the strong Feller…
We develop a discrete spectral framework for Dirichlet $L$-functions that reveals a combinatorial structure underlying their special values and connects this to their zeros. Our approach approximates the classical Dirichlet series by finite…
Starting with a transient irreducible diffusion process $X^0$ on a locally compact separable metric space $(D, d)$, one can construct a canonical symmetric reflected diffusion process $\bar X$ on a completion $D^*$ of $(D, d)$ through the…
We study upper estimates of the martingale dimension $d_m$ of diffusion processes associated with strong local Dirichlet forms. By applying a general strategy to self-similar Dirichlet forms on self-similar fractals, we prove that $d_m=1$…
We develop sufficient analytic conditions for recurrence and transience of non-sectorial perturbations of possibly non-symmetric Dirichlet forms on a general state space. These form an important subclass of generalized Dirichlet forms which…
In the context of the correspondence between real functions on the unit circle and inner analytic functions within the open unit disk, that was presented in previous papers, we show that the constructions used to establish that…
We establish an upper bound of the bottom of the essential spectrum for the generator associated with a regular Dirichlet form in terms of the rates of the volume growth/decay and big jump. Using this bound, we discuss how the bottom of the…
Roughly speaking, the regular subspace of a Dirichlet form is also a regular Dirichlet form on the same state space. It inherits the same form of original Dirichlet form but possesses a smaller domain. What we are concerned in this paper…
After recalling the Dirichlet problem at infinity on a Cartan-Hadamard manifold, we discuss what is known and the difference between the two-dimensional and higher-dimensional cases. Turning our attention to the two-dimensional case, we…
The structural invariant subspaces of the discrete-time singular Hamiltonian system are used in 1] to give an analytic nonrecursive expression of all the admissible trajectories. A deeper insight into the features of these subspaces,…
Given a subset $D$ of the Euclidean space, we study nonlocal quadratic forms that take into account tuples $(x,y) \in D \times D$ if and only if the line segment between $x$ and $y$ is contained in $D$. We discuss regularity of the…
Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…
We extend the generalized gradient-flow framework of Peletier, Rossi, Savar\'e, and Tse to singular jump processes on abstract metric spaces, moving beyond the translation-invariant kernels considered in $\mathbb{R}^d$ and $\mathbb{T}^d$ in…
In this paper, we discuss estimates of transition densities of subordinate Brownian motions in open subsets of Euclidean space. When $D$ is a $C^{1,1}$ domain, we establish sharp two-sided estimates for the transition densities of a large…
We study Dirichlet series enumerating orbits of Cartesian products of maps whose orbit distributions are modelled on the distributions of finite index subgroups of free abelian groups of finite rank. We interpret Euler factors of such orbit…
The present paper studies the Dirichlet spaces in balls and upper-half Euclidean spaces. As main results, we give identical characterizations of the Dirichlet norms in the respective contexts as for the classical 2-D disc case proved by…
Dirichlet processes and their extensions have reached a great popularity in Bayesian nonparametric statistics. They have also been introduced for spatial and spatio-temporal data, as a tool to analyze and predict surfaces. A popular…
The Convex Envelope of a given function was recently characterized as the solution of a fully nonlinear Partial Differential Equation (PDE). In this article we study a modified problem: the Dirichlet problem for the underlying PDE. The main…
We develop sufficient analytic conditions for conservativeness of non-sectorial perturbations of symmetric Dirichlet forms which can be represented through a carr\'e du champ on a locally compact separable metric space. These form an…