Related papers: Residue functions and Extension problems
In this paper we model discontinuous extended real functions in pointfree topology following a lattice-theoretic approach, in such a way that, if $L$ is a subfit frame, arbitrary extended real functions on $L$ are the elements of the…
The rearrangement inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands…
Law-invariant functionals are central to risk management and assign identical values to random prospects sharing the same distribution under an atomless reference probability measure. This measure is typically assumed fixed. Here, we adopt…
This is an extensive (published) survey on CR geometry, whose major themes are: formal analytic reflection principle; generic properties of Systems of (CR) vector fields; pairs of foliations and conjugate reflection identities; Sussmann's…
We investigate the quantitative unique continuation properties of solutions to second-order elliptic equations with lower-order terms. In particular, we establish quantitative forms of the strong unique continuation property for solutions…
Extended real-valued functions are often used in optimization theory, but in different ways for infimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and…
We introduce the homogeneous and piecewise multilinear extensions and the eigenvalue problem for locally Lipschitz function pairs, in order to develop a systematic framework for relating discrete and continuous min-max problems. This also…
We prove that convex functions of finite order on the real line and subharmonic functions of finite order on finite dimensional real space, bounded from above outside of some set of zero relative Lebesgue density, are bounded from above…
A simple test is proposed for examining the correctness of a given completely specified response function against unspecified general alternatives in the context of univariate regression. The usual diagnostic tools based on residuals plots…
In this note, we show how to apply the original $L^2$-extension theorem of Ohsawa and Takegoshi to the standard basis of a multiplier ideal sheaf associated with a plurisubharmonic function. In this way, we are able to reprove the strong…
The property that a one to one function from the natural numbers to itself preserves the density of sub-sets is shown to be equivalent to a condition on the covering of intervals in the range of the function by images of intervals in the…
After a brief review of the historical role of analyticity in the study of critical phenomena, an account is given of recent discoveries of discretely holomorphic observables in critical two-dimensional lattice models. These are objects…
Gleason-type theorems derive the density operator and the Born rule formalism of quantum theory from the measurement postulate, by considering additive functions which assign probabilities to measurement outcomes. Additivity is also the…
Let $\mathcal{X}$ be a subset of $L^1$ that contains the space of simple random variables $\mathcal{L}$ and $\rho: \mathcal{X} \rightarrow (-\infty,\infty]$ a dilatation monotone functional with the Fatou property. In this note, we show…
We study global existence and decay estimates for quasilinear wave equations with dissipative terms in the Sobolev space $H^L \times H^{L-1}$, where $L \geq [d/2]+3$. The linear dissipative terms depend on space variable coefficient, and…
We utilize the Legendre-Fenchel transform and weak geodesics for plurisubharmonic functions to construct a weight function that can be used in the Berndtsson-Lempert method, to give an Ohsawa-Takegoshi extension type of result. Theorem 4.1…
In this paper we are concerned with the space of tempered ultrahyperfunctions corresponding to a proper open convex cone. A holomorphic extension theorem (the version of the celebrated edge of the wedge theorem) will be given for this…
Given a functional central limit (fCLT) for an estimator and a parameter transformation, we construct random processes, called functional delta residuals, which asymptotically have the same covariance structure as the limit process of the…
Under the separability assumption on the augmented density, a distribution function can be always constructed for a spherical population with the specified density and anisotropy profile. Then, a question arises, under what conditions the…
This note reviews the authors' approach to Fujino's conjecture, i.e. the injectivity theorem for lc pairs on compact K\"ahler manifolds, via the use of adjoint ideal sheaves coupled with the associated residue computations in their previous…