相关论文: Non-positivity of Groenewold operators
Physical systems that dissipate, mix and develop turbulence also irreversibly transport statistical density. In statistical physics, laws for these processes have a mathematical form and tractability that depends on whether the description…
Simple and analytically tractable expressions for functional determinants are known to exist for many cases of interest. We extend the range of situations for which these hold to cover systems of self-adjoint operators of the…
We characterize the modular and norm inequalities for the Dunkl-Hausdorff operator defined on non-negative non-increasing functions in the framework of the weighted Orlicz spaces.
In this paper, a positive operator is given. It is shown that the product of this positive operator and the convolution operator is a trace class Hilbert-Schmidt integral operator and has nonnegative eigenvalues. A formula is given for the…
By computing the completely bounded norm of the flip map on the Haagerup tensor product $C_0 Y_1\otimes_{C_0 X} C_0 Y_2$ associated to a pair of continuous mappings of locally compact Hausdorff spaces $Y_1\rightarrow X\leftarrow Y_2$, we…
We address the count of isolated and embedded eigenvalues in a generalized eigenvalue problem defined by two self-adjoint operators with a positive essential spectrum and a finite number of isolated eigenvalues. The generalized eigenvalue…
Two-particle discrete Schr\"{o}dinger operators $H(k)=H_{0}(k)-V$ on the three-dimensional lattice $\Z^3,$ $k$ being the two-particle quasi-momentum, are considered. An estimate for the number of the eigenvalues lying outside of the band of…
We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a…
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new…
We provide the spectral expansion in a weighted Hilbert space of a substantial class of invariant non-self-adjoint and non-local Markov operators which appear in limit theorems for positive-valued Markov processes. We show that this class…
We consider the indefinite Sturm-Liouville differential expression \[\mathfrak{a}(f) := - \frac{1}{w}\left( \frac{1}{r} f' \right)',\] where $\mathfrak{a}$ is defined on a finite or infinite open interval $I$ with $0\in I$ and the…
The Heisenberg picture of the minisuperspace model is considered. The suggested quantization scheme interprets all the observables including the Universe scale factor as the (quasi)Heisenberg operators. The operators arise as a result of…
We apply concepts of random differential geometry connected to the random matrix ensembles of the random linear operators acting on finite dimensional Hilbert spaces. The values taken by random linear operators belong to the Liouville…
We address facts and open questions concerning the degree of ill-posedness of the composite Hausdorff moment problem aimed at the recovery of a function $x \in L^2(0,1)$ from elements of the infinite dimensional sequence space $\ell^2$ that…
We study perturbations of the self-adjoint periodic Sturm--Liouville operator \[ A_0 = \frac{1}{r_0}\left(-\frac{\mathrm d}{\mathrm dx} p_0 \frac{\mathrm d}{\mathrm dx} + q_0\right) \] and conclude under $L^1$-assumptions on the differences…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
This note supplements the work of Gomez-Ullate, Kamran and Milson on the X_(1)-Jacobi polynomials which are orthogonal in a weighted Hilbert function space on the the interval (-1,+1) of the real line. These polynomials are generated by a…
It is shown that the series derived by Mizrahi, giving the Husimi transform (or covariant symbol) of an operator product, is absolutely convergent for a large class of operators. In particular, the generalized Liouville equation, describing…
A curvature inequality is established for contractive commuting tuples of operators in the Cowen-Douglas class of rank n. Properties of the extremal operators, that is, the operators which achieve equality, are investigated. Specifically, a…
Denote by $L_D$ the Sturm-Liouville operator $Ly=-y" +q(x)y$ on the finite interval $[0,\pi]$ with Dirichlet boundary conditions $y(0)=y(\pi)=0$. Let $\{\lambda_k\}_1^\infty$ and $\{\alpha_k\}_1^\infty$ be the sequences of the eigenvalues…