Related papers: Concavity of Eigenvalue Sums and the Spectral Shif…

This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…

We show that Connes' embedding conjecture on von Neumann algebras is equivalent to the existence of certain algebraic certificates for a polynomial in noncommuting variables to satisfy the following nonnegativity condition: The trace is…

We study pseudospectral and spectral functions for Hamiltonian system $Jy'-B(t)=\lambda\Delta(t)y$ and differential equation $l[y]=\lambda\Delta(t)y$ with matrix-valued coefficients defined on an interval $\mathcal{I}=[a,b)$ with the…

A discrete eigenvalue E_n of a Schroedinger operator H = -\Delta + vf(r) is given, as a function F_n(v) of the coupling parameter v\ge v_c. It is shown how the potential shape f(x) can be reconstructed from F_n(v). A constructive inversion…

We prove Lieb type convexity and concavity results for trace functionals associated with positive operator monotone (decreasing) functions and certain monotone concave functions. This gives a partial generalization of Hiai's recent work on…

In this article we proved an interesting property of the class of continuous convex functions. This leads to the form of pre-Hermite-Hadamard inequality which in turn admits a generalization of the famous Hermite-Hadamard inequality. Some…

We consider the inverse eigenvalue problem for entanglement witnesses, which asks for a characterization of their possible spectra (or equivalently, of the possible spectra resulting from positive linear maps of matrices). We completely…

We investigate convexity properties of the set of eigenvalue tuples of $n\times n$ real symmetric matrices, whose all $k\times k$ (where $k\leq n$ is fixed) minors are positive semidefinite. It is proven that the set…

In this paper, the connection between the functional inequalities $$ f\Big(\frac{x+y}{2}\Big)\leq\frac{f(x)+f(y)}{2}+\alpha_J(x-y) \qquad (x,y\in D)$$ and $$ \int_0^1f\big(tx+(1-t)y\big)\rho(t)dt \leq\lambda f(x)+(1-\lambda)f(y)…

In this paper, we introduce the concept of operator geometrically convex functions for positive linear operators and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain trace inequalities for…

Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…

We study the shifted convolution sums associated to completely multiplicative functions taking values in $\{\pm 1\}$ and give combinatorical proofs of two recent results in the direction of Chowla's conjecture. We also determine the…

Let $N$ be a weakly unitarily invariant norm (i.e. invariant for the coadjoint action of the unitary group) in the space of skew-Hermitian matrices $\mathfrak{u}_n(\mathbb C)$. In this paper we study the geometry of the unit sphere of such…

Motivated by considerations of euclidean quantum gravity, we investigate a central question of spectral geometry, namely the question of reconstructability of compact Riemannian manifolds from the spectra of their Laplace operators. To this…

The isospectral reduction of matrix, which is closely related to its Schur complement, allows to reduce the size of a matrix while maintaining its eigenvalues up to a known set. Here we generalize this procedure by increasing the number of…

We consider the sum of two large Hermitian matrices $A$ and $B$ with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is…

In this work, we show how the eigenstructures of summands are related to that of the sum. In particular, we show that the sum of two positive semidefinite matrices can be written as the inner product of two block matrices $\mathbf{C} =…

In this paper we express the eigenvalues of a sort of real heptadiagonal symmetric matrices as the zeros of explicit rational functions establishing upper and lower bounds for each of them. From these prescribed eigenvalues we compute also…

In the following text for vector space $V$ over field $F$ we compute all eigenvalues of weighted generalized shift $\sigma_{\varphi,\mathfrak{w}}:V^\Gamma\to V^\Gamma$ (and generalized shift $\sigma_\varphi:V^\Gamma\to V^\Gamma$) for…

In this paper, we consider the convolutions of slanted half-plane mappings and strip mappings and generalize related results in general settings. We also consider a class of harmonic mappings containing slanted half-plane mappings and strip…