Related papers: Convex Multivariable Trace Functions

This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previously treated in [3] and…

In this paper, some Jensen's type inequalities between quaternionic bounded selfadjoint operators on quaternionic Hilbert spaces are proved, using a log-convex function. Also, by applying a specific log-convex function, some particular…

In this paper we show that every $L^1$-integrable function on $\partial\Omega$ can be obtained as the trace of a function of bounded variation in $\Omega$ whenever $\Omega$ is a domain with regular boundary $\partial\Omega$ in a doubling…

A natural generalization of Krein's theorem to a pair of commuting tuples $\left(H_1^0,H_2^0\right)$ and $\left(H_1,H_2\right)$ of bounded self-adjoint operators in a separable Hilbert space $\mathcal{H}$ with $H_j-H_j^0 = V_j\in…

Polyconvexity is an important concept in the analysis of energies related to elasticity. A function $f \colon \R^{d\times d} \to \R$ is called polyconvex if it can be written as a convex function in the minors of the argument. We show that…

Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…

Given a von Neumann algebra $M$ with a faithful normal semi-finite trace $\tau,$ let $L(M, \tau)$ be the algebra of all $\tau$-measurable operators affiliated with $M.$ We prove that if $A$ is a locally convex reflexive complete metrizable…

This paper is concerned with developing a theory of traces for functions that are integrable but need not possess any differentiability within their domain. Moreover, the domain can have an irregular boundary with cusp-like features and…

We study operator log-convex functions on $(0,\infty)$, and prove that a continuous nonnegative function on $(0,\infty)$ is operator log-convex if and only if it is operator monotone decreasing. Several equivalent conditions related to…

In a recent article (2022) we proved with L. Zaj\'i\v{c}ek that if $ G\subset\R^n $ is an unbounded open convex set that does not contain a translation of a convex cone with non-empty interior, then there exist $ f:G\to\R $ and a concave…

If G is a Lie group, let D(G) be the space of compactly supported smooth functions on G. Consider the bilinear map B : D(G) x D(G) -> D(G), (f,g) |-> f*g which takes a pair of test functions to their convolution. We show that B is…

Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…

We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity…

A convex-polynomial is a convex combination of the monomials $\{1, x, x^2, \ldots\}$. This paper establishes that the convex-polynomials on $\mathbb R$ are dense in $L^p(\mu)$ and weak$^*$ dense in $L^\infty(\mu)$, precisely when…

We obtain operator concavity (convexity) of some functions of two or three variables by using perspectives of regular operator mappings of one or several variables. As an application, we obtain, for $ 0<p < 1,$ concavity, respectively…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^N$. Given a continuous plurisubharmonic function $u$ on $\Omega$, we construct a sequence of Gaussian analytic functions $f_n$ on $\Omega$ associated with $u$ such that…

In metric measure spaces, we study boundary traces of BV functions in domains equipped with a doubling measure and supporting a Poincar\'e inequality, but possibly having a very large and irregular boundary. We show that the trace exists in…

The notion of Ces\`aro stable function is generalized by introducing Ces\`aro mean of type $(b-1;c)$ which give rise to a new concept of generalized Ces\`aro stable function. As an application of generalized Ces\`aro stable functions we…

We construct an analogue of Kontsevich and Vishik's canonical trace for a class of pseudodifferential boundary value problems in Boutet de Monvel's calculus on compact manifolds with boundary. For an operator A in the calculus (of class…

We study the trace functions in orbiford theory for Z-graded vertex operator superalgebras and obtain a modular invariance result. More precisely, let V be a C_2-cofinite Z-graded vertex operator superalgebra and G a finite automorphism…