Related papers: Essential norm of the differential operator

Here we study dilations of q-commuting tuples. In [BBD] the authors gave the correspondence between the two standard dilations of commuting tuples and here these results have been extended to q-commuting tuples. We are able to do this when…

We introduce a noncommutative analogue of the absolute value of a regular operator acting on a noncommutative $\mathrm{L}^p$-space. We equally prove that two classical operator norms, the regular norm and the decomposable norm are…

We give different types of new characterizations for the boundedness and essential norms of generalized weighted composition operators between Zygmund type spaces. Consequently, we obtain new characterizations for the compactness of such…

Motivated by some recent results, but also referring to recognized classics, we compute the essential norm and the weak essential norm of multiplication operators acting between two distinct K{\" o}the spaces both defined over the same…

For a Riemannian covering $p \colon M_{2} \to M_{1}$, we compare the spectrum of an essentially self-adjoint differential operator $D_{1}$ on a bundle $E_{1} \to M_{1}$ with the spectrum of its lift $D_{2}$ on $p^{*}E_{1} \to M_{2}$. We…

Given a dissipative operator $A$ on a complex Hilbert space $\mathcal{H}$ such that the quadratic form $f\mapsto \mbox{Im}\langle f,Af\rangle$ is closable, we give a necessary and sufficient condition for an extension of $A$ to still be…

In this paper we present how spectral properties of certain linear operators vary when operators are considered in different Hilbert spaces having common dense domain as the space of polynomials in one real variable with complex…

We determine necessary and sufficient conditions on the ring of differential operators of a finite purely inseparable field extension of positive characteristic for determining whether the extension is modular.

Using the method of similar operators we study an even order differential operator with periodic, semiperiodic, and Dirichlet boundary conditions. We obtain asymptotic formulas for eigenvalues of this operator and estimates for its spectral…

In this paper, we give some estimates for the norm and essential norm of the differences of two composition operators between different Hardy spaces.

Let $f$ be a function in the inhomogeneous analytic Besov space $B_{\infty,1}^1$. For a pair $(L,M)$ of not necessarily commuting maximal dissipative operators, we define the function $f(L,M)$ of $L$ and $M$ as a densely defined linear…

The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…

We study the essential self-adjointness for real principal type differential operators. Unlike the elliptic case, we need geometric conditions even for operators on the Euclidean space with asymptotically constant coefficients, and we prove…

When ${\cal{D}}: E \rightarrow F$ is a linear differential operator of order $q$ between the sections of vector bundles over a manifold $X$ of dimension $n$, it is defined by a bundle map $\Phi: J_q(E) \rightarrow F=F_0$ that may depend,…

We study uniform Sobolev inequalities for the second order differential operators $P(D)$ of non-elliptic type. For $d\ge3$ we prove that the Sobolev type estimate $\|u\|_{L^q(\mathbb{R}^d)}\le C \|P(D)u\|_{L^p(\mathbb{R}^d)}$ holds with $C$…

Let $T:Y\to X$ be a bounded linear operator between two normed spaces. We characterize compactness of $T$ in terms of differentiability of the Lipschitz functions defined on $X$ with values in another normed space $Z$. Furthermore, using a…

We consider 1d-Dirac operator $\mathcal L_{P,U}$ acting in $\mathbb H=(L_2[0,\pi])^2$ \begin{gather*} \ell(\mathbf y) = B\mathbf y + P(x)\mathbf y,\qquad B = \begin{pmatrix}-i&0\\0&i\end{pmatrix},\\ P(x) = \begin{pmatrix}p_1(x)&p_2(x)\\…

Integral representations of two $q$-difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to $q$-difference equations in the complex domain. Both representations are unified through…

The aim of this paper is to present a survey of some recent results obtained in the study of spaces with asymmetric norm. The presentation follows the ideas from the theory of normed spaces (topology, continuous linear operators, continuous…

The limit $q$-Durrmeyer operator, $D_{\infty,q},$ was introduced and its approximation properties were investigated by V. Gupta in 2008 during a study of $q$-analogues for the Bernstein-Durrmeyer operator. In the present work, this operator…