Related papers: Uncertainty relations and applications in spectral…
This article serves a few purposes. First of all, it reviews polyfold--Kuranishi correspondence I (http://arxiv.org/abs/1402.7008) and previews and samples some results from four papers I have been preparing. It is also a written-up and…
Recent research efforts in optical computing have gravitated towards developing optical neural networks that aim to benefit from the processing speed and parallelism of optics/photonics in machine learning applications. Among these…
This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including…
This is an extended abstract of my talk at the Oberwolfach Workshop ''Cluster Algebras and Related Topics'' (December 8 - 14, 2013). It is based on a joint work with A. Zelevinsky (arXiv:1306.3495).
In recent years, theoretical and phenomenological studies with effective field theories have become a trending and prolific line of research in the field of high-energy physics. In order to discuss present and future prospects concerning…
Following to the Weil method we generalize the Heisenberg-Robertson uncertainty relation for arbitrary two operators. Consideration is made in spherical coordinates, where the distant variable is restricted from one side, . By this reason…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…
One-parameter strongly continuous semigroups of linear bounded operators on Banach spaces (also known as $C_0$-semigroups) are a fundamental operator-theoretic tool used in the study of linear and non-linear evolution PDEs arising in…
We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet…
The main issues of the spectral theory of Dirac operators are presented, namely: transformation operators, asymptotics of eigenvalues and eigenfunctions, description of symmetric and self-adjoint operators in Hilbert space, expansion in…
This is an extended abstract of the talk given in the Oberwolfach miniworkshop "Nichols algebras and Weyl groupoids" in October 2012.
These are lecture notes of a minicourse given by the first author at the Summer School on Quantization at the University of Notre Dame in June 2011. The notes were written up and expanded by the second author who took the liberty of adding…
We review some important algebraic structures which appear in a priori remote areas of Mathematics, such as control theory, numerical methods for solving differential equations, and renormalization in Quantum Field Theory. Starting with…
We derive and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is…
We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…
The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled rank-one perturbations is one of our settings. Spectral…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
The aim of this article is to present a brief overview of spectral perturbation theory for matrices, bounded linear operators and holomorphic operator-valued functions. We focus on bounds for perturbed eigenvalues, eigenvectors and…
This file is composed of questions that emerged or were of interest during the workshop "Interactions between Descriptive Set Theory and Smooth Dynamics" that took place in Banff, Canada on 2022.