Cardona Sanchez, Duvan

In this note, we study the mapping properties of global pseudo-differential operators with symbols in Ruzhansky-Turunen classes on Besov spaces B-infinity,infinity(s)(G). The considered classes satisfy Fefferman type conditions of limited regularity.

Ruzhansky, Michael Tokmagambetov, Niyaz

In this paper we study the Cauchy problem for the semilinear damped wave equation for the sub-Laplacian on the Heisenberg group. In the case of the positive mass, we show the global in time well-posedness for small data for power like nonlinearities. We also obtain similar well-posedness results for the wave equations for Rockland operators on gene...

Bingham, NH Ostaszewski, AJ

The theme here is category-measure duality, in the context of a topological group. One can often handle the (Baire) category case and the (Lebesgue, or Haar) measure cases together, by working bi-topologically: switching between the original topology and a suitable refinement (a density topology). This prompts a systematic study of such density top...

Talpo, Mattia Vistoli, Angelo

We define and study infinite root stacks of fine and saturated logarithmic schemes, a limit version of the root stacks introduced by Niels Borne and the second author. We show in particular that the infinite root stack determines the logarithmic structure, and recovers the Kummer-flat topos of the logarithmic scheme. We also extend the corresponden...

Talpo, Mattia Vistoli, Angelo
Published in
Bollettino dell'Unione Matematica Italiana

We extend the formalism of “log spaces” of Gillam and Molcho (Log differentiable spaces and manifolds with corners. arXiv:1507.06752, 2015) to topoi equipped with a sheaf of monoids, and discuss Deligne–Faltings structures and root stacks in this context.

Donaldson, Simon Sun, Song

We study Gromov–Hausdorff limits of Kähler–Einstein manifolds, in particular, their singularities, and connections with algebraic geometry. This is a continuation of our previous work.

Jacob, Birgit Partington, Jonathan R. Pott, Sandra Wynn, Andrew
Published in
Journal of Evolution Equations

We prove a Weiss conjecture on β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-admissibility of observation operators for discrete and continuou...

Betancourt, M Byrne, S Livingstone, S Girolami, M

Although Hamiltonian Monte Carlo has proven an empirical success, the lack of a rigorous theoretical understanding of the algorithm has in many ways impeded both principled developments of the method and use of the algorithm in practice. In this paper, we develop the formal foundations of the algorithm through the construction of measures on smooth...

Beskos, A Girolami, M Lan, S Farrell, PE Stuart, AM

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce st...

Siorpaes, P

In this paper, after generalizing the pathwise Burkholder–Davis–Gundy (BDG) inequalities from discrete time to cadlag semimartingales, we present several applications of the pathwise inequalities. In particular we show that they allow to extend the classical BDG inequalities 1. to the Bessel process of order α ≥ 1 2. to the case of a random exponen...