Related papers: Hairer's Reconstruction Theorem without Regularity…

These expository notes, addressed to non-experts, are intended to present some of Hironaka's ideas on his theorem of resolution of singularities. We focus particularly on those aspects which have played a central role in the constructive…

A new formalism is given for the renormalization of quantum field theories to all orders of perturbation theory, in which there are manifestly no overlapping divergences. We prove the BPH theorem in this formalism, and show how the local…

Student's theorem is an important result in statistics which states that for normal population, the sample variance is independent from the sample mean and has a chi-square distribution. The existing proofs of this theorem either overly…

Using the Hilbert-Schmidt theorem, we reformulate the R-matrix theory in terms of a uniformly and absolutely convergent expansion. Term by term differentiation is possible with this expansion in the neighborhood of the surface. Methods for…

By extrapolating the explicit formula of the zero-bias distribution occurring in the context of Stein's method, we construct characterization identities for a large class of absolutely continuous univariate distributions. Instead of trying…

Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. It allows one to recover any element in any finite-dimensional subspace given finitely many of its samples with…

A very particular by-product of the result announced in the title reads as follows: Let $(X,<\cdot,\cdot>)$ be a real Hilbert space, $T:X\to X$ a compact and symmetric linear operator, and $z\in X$ such that the equation $T(x)-\|T\|x=z$ has…

Cut-elimination theorems constitute one of the most important classes of theorems of proof theory. Since Gentzen's proof of the cut-elimination theorem for the system $\mathbf{LK}$, several other proofs have been proposed. Even though the…

This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a…

We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…

We develop a regularity and compactness theory for stable capillary minimal hypersurfaces in the half-space $\mathbb{H}^{n+1}$ with contact angle $\theta \in (0,\pi)$ and dimension $n \geq 2$. As a consequence, we obtain the generalized…

The main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical Hough transform and extend them to general algebraic objects such as affine schemes. The main motivation comes from…

Hilbert's Irreducibility Theorem is a cornerstone that joins areas of analysis and number theory. Both the genesis and genius of its proof involved combining real analysis and combinatorics. We try to expose the motivations that led Hilbert…

In this paper, we establish an analog of Wightman's reconstruction theorem for nonlocal quantum field theory with a fundamental length. In our setting, the Wightman generalized functions are defined on test functions analytic in a complex…

We revisit the partial $\mathrm{C}^{1,\alpha}$ regularity theory for minimizers of non-parametric integrals with emphasis on sharp dependence of the H\"older exponent $\alpha$ on structural assumptions for general zero-order terms. A…

We study parameter identification problems in a structured population model without mutations. Given measurements of the total population size or critical points of the population, we aim to recover its growth rate, death rate or initial…

An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what…

We review the theory of renormalization, including perturbative renormalization, regularized functional integrals, Renormalization Group and rigorous renormalization.

The main result of this paper is that every naturally reductive space can be explicitly constructed from the construction in \cite{Storm2018}. This gives us a general formula for any naturally reductive space and from this we prove…

We investigate the structure of return-time sets determined by orbits along polynomial tuples in minimal topological dynamical systems. Building on the topological characteristic factor theory of Glasner, Huang, Shao, Weiss, and Ye, we…