相关论文: A non commutative sewing lemma

This paper treatises the preservation of some spectra under perturbations not necessarily commutative and generalizes several results which have been proved in the case of commuting operators.

The lefthanded Lov\'asz local lemma (LLLL) is a generalization of the Lov\'asz local lemma (LLL), a powerful technique from the probabilistic method. We prove a computable version of the LLLL and use it to effectivize a collection of…

We present a description of the (non-modular) commutator, inspired by that of Kearnes in~\cite[p.~930]{MR1358491}, that provides a simple recipe for computing the commutator.

For a general class of contractions of a variety X to a base Y, I discuss recent joint work with M. Wemyss defining a noncommutative enhancement of the locus in Y over which the contraction is not an isomorphism, along with applications to…

We apply the dressing method on the Non Linear Sigma Model (NLSM), which describes the propagation of strings on $\mathbb{R}\times \mathrm{S}^2$, for an arbitrary seed. We obtain a formal solution of the corresponding auxiliary system,…

We give a constructive, metastable formulation of a theorem about the exchange of limits for convergent sequence $L^1$ functions. A crucial tool is a one-dimensional version of Szemeredi's regularity lemma for $L^1$ functions.

We discuss technical results on learning function approximations using piecewise-linear basis functions, and analyze their stability and convergence using nonlinear contraction theory.

We prove that the non-commutative perspective of an operator convex function is the unique extension of the corresponding commutative perspective that preserves homogeneity and convexity.

We give some details about the stationary phase lemma. We first prove a special case where the high order terms are derived explicitly. Based on that, we prove a more general case by using Morse lemma.

We present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk-Ulam theorem perspective.

We extend Hadamard's Lemma to the setting of a separable Hilbert space.

In this article we prove a Grothendieck trace formula for L-functions of not necessarily commutative adic sheaves.

This paper extends some results on the S-Lemma proposed by Yakubovich and uses the improved results to investigate the asymptotic stability of a class of switched nonlinear systems. Firstly, the strict S-Lemma is extended from quadratic…

This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables.…

We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…

By viewing non-commutative polynomials, that is, elements in free associative algebras, in terms of linear representations, we generalize Horner's rule to the non-commutative (multivariate) setting. We introduce the concept of Horner…

We give a precise, computable formula for comparing $\lambda$-invariants between modular forms in the anticyclotomic indefinite setting where the Selmer groups have positive rank. This is an improvement of Hatley-Lei \cite{HL19, HL21} where…

As a first step at developing a theory of noncommutative nonlinear elliptic partial differential equations, we analyze noncommutative analogues of Laplace's equation and its variants (some of the them nonlinear) over noncommutative tori.…

We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…

We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…