Related papers: On some problems concerning symmetrization operato…
Truncated Toeplitz operators in a model space are C--symmetric with respect to a natural conjugation in that space. We show that this and another conjugation associated to an orthogonal decomposition possess unique properties and we study…
This is an ultimate completion of our earlier paper [Acta.\ Math.\ Hungar.\ 140 (2013), 248--292] where mapping properties of several fundamental harmonic analysis operators in the setting of symmetrized Jacobi trigonometric expansions were…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…
Generalising the definition to commuting $d$-tuples of operators, a number of authors have considered structural properties of $m$-isometric, $n$-symmetric and $(m,n)$-isosymmetric commuting $d$-tuples in the recent past. This note is an…
Motivated by the existence of cyclic phenomena in which some characteristics are mapped into corresponding ones over more than one phase, we introduce the $r$-cyclic operators with respect to a covering of a metric space and investigate…
This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex) functions have been proved. Several special…
In light of the log-Brunn-Minkowski conjecture, various attempts have been made to define the geometric mean of convex bodies. Many of these constructions are fairly complex and/or fail to satisfy some natural properties one would expect of…
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…
We extend to larger unification groups an earlier study exploring the possibility of unification of gauge symmetries in theories with dynamical symmetry breaking. Based on our results, we comment on the outlook for models that seek to…
In this paper we survey some recent works that take the first steps toward establishing bilateral connections between symplectic geometry and several other fields, namely, asymptotic geometric analysis, classical convex geometry, and the…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
We propose a general convex optimization problem for computing regularized geodesic distances. We show that under mild conditions on the regularizer the problem is well posed. We propose three different regularizers and provide analytical…
In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and…
The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…
The problem of equivalency for linear differential operators of the first order is discussed.
We focus on the linear convergence of generalized proximal point algorithms for solving monotone inclusion problems. Under the assumption that the associated monotone operator is metrically subregular or that the inverse of the monotone…
Consider a sum of convex functions, where the only information known about each individual summand is the location of a minimizer. In this work, we give an exact characterization of the set of possible minimizers of the sum. Our results…
Several aspects of the interplay between monotone operator theory and convex optimization are presented. The crucial role played by monotone operators in the analysis and the numerical solution of convex minimization problems is emphasized.…