Related papers: A refined transversality theorem on linear perturb…

We present a slightly simpler proof of the multilinear refined Strichartz estimate, and prove a slightly more general linear refined Strichartz estimate. Our arguments seek to clarify the connection between these estimates, refined…

This paper deals with perturbation theory for discrete spectra of linear operators. To simplify exposition we consider here self-adjoint operators. This theory is based on the Feshbach-Schur map and it has advantages with respect to the…

We give a Herglotz-type representation of an arbitrary generalized spectral measure. As an application, a new proof of the classical Naimark's dilation theorem is given. The same approach is used to describe the spectrum of all unitary…

We introduce N-parameter perturbation theory as a new tool for the study of non-linear relativistic phenomena. The main ingredient in this formulation is the use of the Baker-Campbell-Hausdorff formula. The associated machinery allows us to…

A Lagrange multiplier theorem is derived for the case of an imprecise objective function and a precise constraint. The proof uses methods of analysis which deal in a direct, algebraic way with imprecisions. They include imprecise…

We prove a general extension theorem for holomorphic line bundles on reduced complex spaces, equipped with singular hermitian metrics, whose curvature currents can be extended as positive, closed currents. The result has applications to…

This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…

In this paper we use the strength of the constraint method in combination with a generalized Borsuk-Ulam type theorem and a cohomological intersection lemma to show how one can obtain many new topological transversal theorems of Tverberg…

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…

Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. After reviewing the general framework of the second-order gauge-invariant perturbation theory, we show the fact that…

Calculations of high-energy processes involving the production of a large number of particles in weakly-coupled quantum field theories have previously signaled the need for novel non-perturbative behavior or even new physical phenomena. In…

The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…

We consider small perturbations of a conformal iterated function system (CIFS) produced by either adding or removing some generators with small derivative from the original. We establish a formula, utilizing transfer operators arising from…

The article summarizes some developments about a singular versions of the Sturm Comparison and Separation theorems where the coefficients or the interval of definition may be unbounded.

For the importance of differentiation theorems in metric spaces (starting with Pansu Rademacher type theorem in Carnot groups) and relations with rigidity of embeddings see the section 1.2 in Cheeger and Kleiner paper arXiv:math/0611954 and…

This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…

We show here that the refined theorems for both lecture hall partitions and anti-lecture hall compositions can be obtained as straightforward consequences of two q-Chu Vandermonde identities, once an appropriate recurrence is derived. We…

We establish extension theorems for separately holomorphic mappings defined on sets of the form W\setminus M with values in a complex analytic space which possesses the Hartogs extension property. Here W is a 2-fold cross of arbitrary…

In this work we pursue the singular-vector analysis of the integrable perturbations of conformal theories that was initiated in hep-th/9603088. Here we consider the detailed study of the N=1 superconformal theory and show that all…

We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results obtained…