Related papers: Minimal projections with respect to various norms
It was shown in Bj\"orn--Bj\"orn--Korte ("Minima of quasisuperminimizers", Nonlinear Anal. 155 (2017), 264-284) that $u:=\min\{u_1,u_2\}$ is a $\overline{Q}$-quasisuperminimizer if $u_1$ and $u_2$ are $Q$-quasisuperminimizers and…
This paper establishes several new inequalities for the $A$-norm and $A$-numerical radius of operator sums in semi-Hilbertian spaces, significantly advancing the existing theory. We present two fundamental refinements of the generalized…
We fully characterize orthogonal projections of infinite right circular (round) cones in real Hilbert spaces. Another interpretation is that, given two vectors in a real Hilbert space, we establish the optimal estimate on the angle between…
This paper investigates a refinement of Marstrand's projection theorem; more specifically, let $\Pi_t, t\in[0,1]$ be a family of $m$ dimensional subspaces of the Euclidean space $\mathbb{R}^n$ and let $P_t:\mathbb{R}^4\mapsto \Pi_t$ be the…
We prove a restricted projection theorem for a certain one dimensional family of projections from $\mathbb R^n$ to $\mathbb R^k$. The family we consider here arises naturally in the study of quantitative equidistribution problems in…
Several algebraic and topological properties of subgradient projection operators are investigated and various examples are provided. Connections with Moreau's proximity operator are also made and acceleration schemes for subgradient…
Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
We develop some tools for manipulating and constructing projections in C*-algebras. These are then applied to give short proofs of some standard projection homotopy results, as well as strengthen some fundamental classical results for…
Using techniques from semidefinite programming, we study the problem of finding a closest quantum channel to the projection onto a matricial subsystem. We derive two invariants of matricial subsystems which are related to the quantum…
In this note we show how improved $L^p$-estimates for certain types of quasi-modes are naturally equaivalent to improved operator norms of spectral projection operators associated to shrinking spectral intervals of the appropriate scale.…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
We show that the operator norm of an arbitrary bivariate polynomial, evaluated on certain spectral projections of spin operators, converges to the maximal value in the semiclassical limit. We contrast this limiting behavior with that of the…
This article develops a general theory for minimum norm interpolating estimators and regularized empirical risk minimizers (RERM) in linear models in the presence of additive, potentially adversarial, errors. In particular, no conditions on…
In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying…
Let $R$ be a commutative ring. An $R$-module $M$ is said to be almost projective if ${\rm Ext}^1_R(M, N) = 0$ for any $R_{\mathfrak{m}}$-module $N$ and any maximal ideal $\mathfrak{m}$ of $R$. In this paper, we investigate rings $R$ over…
We extend the Cone Theorem of the Log Minimal Model Program to log varieties with arbitrary singularities.
Quantum mechanical models with a minimal length are often described by modifying the commutation relation between position and momentum. Although this represents a small complication when described in momentum space, at least formally, the…
We prove finite-field analogs of Bourgain's projection theorem in higher dimensions. In particular, for a certain range of parameters we improve on an exceptional set estimate by Chen in all dimensions and codimensions.
Averaging certain class of quasiperiodic monotone operators can be simplified to the periodic homogenization setting by mapping the original quasiperiodic structure onto a periodic structure in a higher dimensional space using cut-and…