Related papers: Inertia indices and eigenvalue inequalities for He…

In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite--Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of…

Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…

Pickrell has fully characterized the unitarily invariant probability measures on infinite Hermitian matrices, and an alternative proof of this classification has been found by Olshanski and Vershik. Borodin and Olshanski deduced from this…

We prove an inequality for unitarily invariant norms that interpolates between the Arithmetic-Geometric Mean inequality and the Cauchy-Schwarz inequality.

In this paper we study eigenvalues of the closed eigenvalue problem of the Witten-Laplacian on an $n$-dimensional compact Riemannian manifold. Estimates for eigenvalues are given. As applications, we give a sharp upper bound for the…

The aim of this paper is to obtain new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. These inequalities give us the possibility to derive estimates from below of the first…

We introduce and study Laplacians on a finite metric graph endowed with generalized densities, that is, measures of finite mass. One important motivation is that this setting provides a common framework for several interesting classes of…

In this paper, we give a symplectic proof of the Horn inequalities on eigenvalues of a sum of two Hermitian matrices with given spectra. Our method is a combination of tropical calculus for matrix eigenvalues, combinatorics of planar…

Our topological setting is a smooth compact manifold of dimension two or higher with smooth boundary. Although this underlying topological structure is smooth, the Riemannian metric tensor is only assumed to be bounded and measurable. This…

Let F be a 4-regular graph with an Euler system C. We introduce a simple way to modify the interlacement matrix of C so that every circuit partition P of F has an associated modified interlacement matrix M(C,P). If C and C' are Euler…

In this paper, we establish several new inequalities for twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

In this paper, we give estimates for both upper and lower bounds of eigenvalues of a simple matrix. The estimates are shaper than the known results.

Determining and analyzing the spectra of graphs is an important and exciting research topic in theoretical computer science. The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on…

Based on the relationship of symmetric operators with Hermitian symmetric spaces, we introduce the notion of \emph{Weyl curve} for a symmetric operator $T$, which is the geometric abstraction and generalization of the well-known Weyl…

We generalise the inference procedure for eigenvectors of symmetrizable matrices of Tyler (1981) to that of invariant and singular subspaces of non-diagonalizable matrices. Wald tests for invariant vectors and $t$-tests for their individual…

Different variants of approximate inverse iteration like the locally optimal block preconditioned conjugate gradient method became in recent years increasingly popular for the solution of the large matrix eigenvalue problems arising from…

Inspired by the recent work by R.Pal et al., we give further refined inequalities for a convex Riemann integrable function, applying the standard Hermite-Hadamard inequality. Our approach is different from their one in \cite{PSMA2016}. As…

On a finite connected metric graph, we establish upper bounds for the eigenvalues of the Laplacian. These bounds depend on the length, the Betti number, and the number of pendant vertices. For trees, these estimates are sharp. We also…

Recently Rohleder proposed a new variational approach to an inequality between the Neumann and Dirichlet eigenvalues in the simply connected planar case using the language of classical vector analysis. Writing his approach in terms of…

Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hard computations specific to the model in…