相关论文: A non-type (D) linear isometry
In this paper, we deal with the inverse problem of the shape reconstruction of inclusions in elastic bodies. The main idea of this reconstruction is based on the monotonicity property of the Neumann-to-Dirichlet operator presented in a…
We give a self-contained and introductory account of some basic functional analytic tools needed to understand maximal monotone operators in Hilbert spaces. We review domains of (possibly unbounded) operators, closed sets and closed…
The present paper is a sequel to our paper "Metric characterization of isometries and of unital operator spaces and systems". We characterize certain common objects in the theory of operator spaces (unitaries, unital operator spaces,…
Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…
We construct small cylinders for cellular non-symmetric DG-operads over an arbitrary commutative ring by using the basic perturbation lemma from homological algebra. We show that our construction, applied to the A-infinity operad, yields…
In this paper, we improve the famous Reid Inequality related to linear operators. Some monotony results for positive operators are also established with a different approach from what is known in the existing literature. Lastly, Reid and…
Given a linear semi-bounded symmetric operator $S\ge -\omega$, we explicitly define, and provide their nonlinear resolvents, nonlinear maximal monotone operators $A_\Theta$ of type $\lambda>\omega$ (i.e. generators of one-parameter…
Maximally monotone operators are fundamental objects in modern optimization. The main classes of monotone operators are subdifferential operators and matrices with a positive semidefinite symmetric part. In this paper, we study a nice class…
Two discretizations, linear and nonlinear, of basic notions of the complex analysis are considered. The underlying lattice is an arbitrary quasicrystallic rhombic tiling of a plane. The linear theory is based on the discrete Cauchy-Riemann…
We focus on the linear convergence of generalized proximal point algorithms for solving monotone inclusion problems. Under the assumption that the associated monotone operator is metrically subregular or that the inverse of the monotone…
Let $X$ be a real reflexive Banach space and $X^*$ be its dual space. Let $G_1$ and $G_2$ be open subsets of $X$ such that $\bar G_2\subset G_1$, $0\in G_2$, and $G_1$ is bounded. Let $L: X\supset D(L)\to X^*$ be a densely defined linear…
It is pointed out that physically meaningful aligned Petrov type D perfect fluid space-times with constant zero-order Riemann invariants are either the homogeneous solutions found by G\"{o}del (isotropic case) and Farnsworth and Kerr…
We treat an inverse electrical conductivity problem which deals with the reconstruction of nonlinear electrical conductivity starting from boundary measurements in steady currents operations. In this framework, a key role is played by the…
In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator $T$ with the Hardy and Copson operators in weighted Lebesgue spaces are proved. New equivalence theorems are obtained for…
The principal innovative idea in this paper is to transform the original complex nonlinear modeling problem into a combination of linear problem and very simple nonlinear problems. The key step is the generalized linearization of nonlinear…
The nonlinear geometry of operator spaces has recently started to be investigated. Many notions of nonlinear embeddability have been introduced so far, but, as noticed before by other authors, it was not clear whether they could be…
The main purpose of this paper is to formulate new conditions for smooth linearization of nonautonomous systems with discrete and continuous time. Our results assume that the linear part admits a very general form of dichotomy known as…
We theoretically investigate the possibility of realizing a nonlinear all-optical diode by using the unique features of quasiperiodic 1D photonic crystals. The interplay between the intrinsic spatial asymmetry in odd-order Thue-Morse…
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…
An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with…