Related papers: Some Aspects of Boolean Valued Analysis
This is a survey of some recent applications of Boolean valued models of set theory to order bounded operators in vector lattices.
The paper contains two main results that are obtained by Boolean valued analysis. The first asserts that a universally complete vector lattice without locally one-dimensional bands can be decomposed into a direct sum of two vector…
We apply the machinery of projection lattices and von Neumann algebras to analyze the question of how modal interpretations can (and do) circumvent von Neumann's infamous 'no-hidden-variables' theorem.
The aim of this paper is to give an extension of the improved Sobolev embedding theorem for single-valued functions to the case of vector-valued functions which is involved with the three-dimensional massless Dirac operator together with…
In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
This is an overview of the recent results of interaction of Boolean valued analysis and vector lattice theory.
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…
We prove by means of advanced pseudo-monotonicity methods an abstract existence result for parabolic partial differential equations with $\log$-H\"older continuous variable exponent nonlinearity governed by the symmetric part of a gradient…
The Wigner-von Neumann method, which was previously used for perturbing continuous Schr\"{o}dinger operators, is here applied to their discrete counterparts. In particular, we consider perturbations of arbitrary $T$-periodic Jacobi…
In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
The general spectral boundary value problem framework is utilized to restate boundary value problems of Poincare, Hilbert, and Riemann for harmonic and analytic functions in abstract operator-theoretic terms.
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…
As more of topology's tools become popular in analyzing high dimensional data sets, the goal of understanding the underlying probabilistic properties of these tools becomes even more important. While much attention has been given to…
Classification theorems for linear differential equations in two real variables, possessing eigenfunctions in the form of the polynomials (the generalized Bochner problem) are given. The main result is based on the consideration of the…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
We use the Foldy--Wouthuysen (unitary) transformation to give an alternative characterization of the eigenvalues and eigenfunctions for the Brown-Ravenhall operator (the projected Dirac operator) in the case of a one-electron atom. In…
Valuations, as additive functionals, allow various applications in Stochastic Geometry, yielding mean value formulas for specific random closed sets and processes of convex or polyconvex particles. In particular, valuations are especially…
After carrying out an overview on the non Euclidean geometrical setting suitable for the study of Kolmogorov operators with rough coefficients, we list some properties of the functional space $\mathcal{W}$, mirroring the classical $H^1$…