Related papers: Majorization and a Schur-Horn Theorem for positive…

In this paper, the concept of grand variable Herz-Morrey-Hardy spaces are introduced. We also establish the atomic characterization of these spaces. As an application the authors investigate the continuity of a few singular integral…

Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein spaces. Under the assumption that 0 and $\infty$ are not singular critical points of…

The unitary equivalence of $2$-isometric operators satisfying the so-called kernel condition is characterized. It relies on a model for such operators built on operator valued unilateral weighted shifts and on a characterization of the…

Using the recent theory of Krein--von Neumann extensions for positive functionals we present several simple criteria to decide whether a given positive functional on the full operator algebra is normal. We also characterize those…

We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of…

We study invertibility and compactness of positive Toeplitz operators associated to a continuous Parseval frame on a Hilbert space. As applications, we characterize compactness of affine and Weyl-Heisenberg localization operators as well as…

For a given C*-algebra $\mathcal{A}$, we establish the existence of maximal and minimal operator $\mathcal{A}$-system structures on an AOU $\mathcal{A}$-space. In the case $\mathcal{A}$ is a W*-algebra, we provide an abstract…

We prove maximal regularity results in H\"older and Zygmund spaces for linear stationary and evolution equations driven by a large class of differential and pseudo-differential operators L, both in finite and in infinite dimension. The…

We obtain the existence, nonexistence and multiplicity of positive solutions with prescribed mass for nonlinear Schr\"{o}dinger equations in bounded domains via a global bifurcation approach. The nonlinearities in this paper can be mass…

In this paper the asymmetric generalization of the Glazman-Povzner-Wienholtz theorem is proved for one-dimensional Schr\"{o}dinger operators with strongly singular matrix potentials from the space $H_{loc}^{-1}(\mathbb{R},…

Eigenvalue problems for semidefinite operators with infinite dimensional kernels appear for instance in electromagnetics. Variational discretizations with edge elements have long been analyzed in terms of a discrete compactness property. As…

We deal with kernel theorems for modulation spaces. We completely characterize the continuity of a linear operator on the modulation spaces $M^p$ for every $1\leq p\leq\infty$, by the membership of its kernel to (mixed) modulation spaces.…

Weyl-von Neumann Theorem asserts that two bounded self-adjoint operators $A,B$ on a Hilbert space $H$ are unitarily equivalent modulo compacts, i.e., $uAu^*+K=B$ for some unitary $u\in \mathcal{U}(H)$ and compact self-adjoint operator $K$,…

We show that formal Schr\"odinger operators with singular potentials from the space W^{-1}_{2,unif}(R) can be naturally defined to give selfadjoint and bounded below operators, which depend continuously in the uniform resolvent sense on the…

It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition if and only if it is non-invertible and has simple spectrum…

In this work sufficient conditions on the order of the symbol are developed to ensure boundedness, compactness and r-nuclearity of pseudo-differential operators in $\hbar\mathbb{Z}^n$. In addition, these conditions allow us to obtain growth…

Let $L$ be a linear, closed, densely defined in a Hilbert space operator, not necessarily selfadjoint. Consider the corresponding wave equations &(1) \quad \ddot{w}+ Lw=0, \quad w(0)=0,\quad \dot{w}(0)=f, \quad \dot{w}=\frac{dw}{dt}, \quad…

In this paper, we are concerned with the Neumann problem for a class of quasilinear stationary Kirchhoff-type potential systems, which involves general variable exponents elliptic operators with critical growth and real positive parameter.…

In [19] there is an approach to the investigation of the pseudocontinuability of Schur functions in terms of Schur parameters. In particular, there was obtained a criterion for the pseudocontinuability of Schur functions and the Schur…

In this paper we consider higher order Schr\"odinger operators $$\mathcal L u=Lu+Vu,$$ where $L$ denotes a fourth order operator and $V\geq 0$ a suitable potential. We initiate our analysis by considering the constant coefficients…