Related papers: Nonlinear Maximal Monotone Extensions of Symmetric…

The paper introduces unbounded antilinear operators on Hilbert spaces and develops their fundamental theory. In particular, we establish a closed range theorem, a polar decomposition theorem, and the convexity of the numerical range for…

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar's constraint qualification holds. In this paper, we…

Let $A$ be a positive bounded linear operator acting on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$. Let $\omega_A(T)$ and ${\|T\|}_A$ denote the $A$-numerical radius and the $A$-operator seminorm of an…

The Borichev--Tomilov theorem \cite{BT2010} provides a sharp characterization of polynomial decay for linear $C_0$-semigroups in terms of resolvent growth along the imaginary axis. In the nonlinear setting, the absence of a spectral theory…

Monotone operators are of basic importance in optimization as they generalize simultaneously subdifferential operators of convex functions and positive semidefinite (not necessarily symmetric) matrices. In 1970, Asplund studied the additive…

Given a densely defined skew-symmetric operators A 0 on a real or complex Hilbert space V , we parametrize all m-dissipative extensions in terms of contractions $\Phi$ : H-$\rightarrow$ H + , where Hand H + are Hilbert spaces associated…

We give an elementary symmetric function expansion for $M\Delta_{m_\gamma e_1}\Pi e_\lambda^{\ast}$ and $M\Delta_{m_\gamma e_1}\Pi s_\lambda^{\ast}$ when $t=1$ in terms of what we call $\gamma$-parking functions and lattice $\gamma$-parking…

Let $\Omega \subset \mathbb{R}^d$ be bounded with $C^1$ boundary. In this paper we consider Schr\"odinger operators $-\Delta+ W$ on $\Omega$ with $W(x)\approx\mathrm{dist}(x, \partial\Omega)^{-2}$ as $\mathrm{dist}(x, \partial\Omega)\to 0$.…

The simplest and most natural examples of completely nonunitary contractions on separable complex Hilbert spaces which have polynomial characteristic functions are the nilpotent operators. The main purpose of this paper is to prove the…

Let $A$ be a positive definite operator on a Hilbert space $H$, and $|||.|||$ be a unitarily invariant norm on $B(H)$. We show that if $f$ is an operator monotone function on $(0,\infty)$ and $n\in \mathbb{N}$, then $|||D^n…

In this paper, we are interested in studying the asymptotic behavior of the solutions of differential inclusions governed by maximally monotone operators. In the case where the LaSalle's invariance principle is inconclusive, we provide a…

Let the complex reflection group $G(m,p,n)$ act on the unit polydisc $\mathbb D^n$ in $\mathbb C^n.$ A $\boldsymbol\Theta_n$-contraction is a commuting tuple of operators on a Hilbert space having…

Let (H_t) be the Ornstein-Uhlenbeck semigroup on R^d with covariance matrix I and drift matrix \lambda(R-I), where \lambda>0 and R is a skew-adjoint matrix and denote by \gamma_\infty the invariant measure for (H_t). Semigroups of this form…

Consider a quasi-periodic Schr\"odinger operator $H_{\alpha,\theta}$ with analytic potential and irrational frequency $\alpha$. Given any rational approximating $\alpha$, let $S_+$ and $S_-$ denote the union, respectively, the intersection…

We construct $\Delta$-operators $F[\Delta]$ on the space of almost symmetric functions $\mathscr{P}_{as}^{+}$. These operators extend the usual $\Delta$-operators on the space of symmetric functions $\Lambda \subset \mathscr{P}_{as}^{+}$…

We consider local "complementary" generalized Morrey spaces ${\dual \cal M}_{\{x_0\}}^{p(\cdot),\om}(\Om)$ in which the $p$-means of function are controlled over $\Om\backslash B(x_0,r)$ instead of $B(x_0,r)$, where $\Om \subset \Rn$ is a…

We study a linear elliptic differential operator of the form $\mathcal{P}=\Delta + V - \lambda$ on a quasi-asymptotically conical manifold $(M, g)$, where $g$ is a polyhomogeneous metric and $V$ is a $b$-vector field that is unbounded with…

Using boundary triples, we develop an abstract framework to investigate the complete non-selfadjointness of the maximally dissipative extensions of dissipative operators of the form $S+iV$, where $S$ is symmetric with equal finite defect…

In this paper we prove some new results and give new proofs of known results related to the large coupling limit for stationary Schr\"odinger operators. The operators we consider are of the form $-\Delta +\lambda V(x)$ where $\Delta$ is the…

In this paper, we describe the leftmost eigenvalue of the non-selfadjoint operator $\mathcal{A}_h = -h^2\Delta+iV(x)$ with Dirichlet boundary conditions on a smooth bounded domain $\Omega\subset\mathbb{R}^n\,$, as $h\rightarrow0\,$. $V$ is…