Related papers: On an assertion about Nash--Moser applications

We establish the following converse of the well-known inverse function theorem. Let $g:U\to V$ and $f:V\to U$ be inverse homeomorphisms between open subsets of Banach spaces. If $g$ is differentiable of class $C^p$ and $f$ if locally…

We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the…

Given any short immersion from an $n$-dimensional bounded and simply connected domain into $\mathbb{R}^{n+1}$ and any H\"older exponent $\alpha<(1+n^2-n)^{-1}$, we construct a $C^{1, \alpha}$ isometric immersion arbitrarily close in the…

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

Using Bauer's expansion and properties of spherical Bessel and Legender functions, we deduce a new transform and briefly indicate its use.

It is shown that the restrictions of what can be inferred from classically-recorded observational outcomes that are imposed by the no-cloning theorem, the Kochen-Specker theorem and Bell's theorem also follow from restrictions on inferences…

Conventional classical confidence intervals in specific cases are unphysical. A solution to this problem has recently been published by Feldman and Cousins. We show that there are cases where the new approach is not applicable and that it…

Recent arguments, involving entangled systems shared by sets of Wigner's friend arrangements, allegedly show that the assumption that the experiments performed by the friends yield definite outcomes, is incompatible with quantum…

In this paper we describe the implementation that led to the counterexamples to the Nash blowup conjectures recently discovered by the authors. We also provide new examples of toric varieties with prescribed singularities that are not…

We give a new proof of quantum Shannon-McMillan theorem, extending it to AF $C^*$-systems. Our proof is based on the variational principle, instead of the classical Shannon-McMillan theorem.

In a nutshell, we intend to extend Schoenberg's classical theorem connecting conditionally positive semidefinite functions $F\colon \mathbb{R}^n \to \mathbb{C}$, $n \in \mathbb{N}$, and their positive semidefinite exponentials $\exp(tF)$,…

It is proven an analogue of The Theorem of Moser according to an iterative normalization procedure depending on Generalized Fischer Decompositions.

In this short note we show how the higher index theory can be used to prove results concerning the non-existence of complete riemannian metric with uniformly positive scalar curvature at infinity. By improving some classical results due to…

We give some new congruences for singular real algebraic curves which generalize Fiedler's congruence for nonsingular curves.

We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.

The main purpose of this article is to provide new results on algebraic independence of values of Mahler functions and their generalizations. Simultaneously, we establish new measures of algebraic independence for these values. Among the…

We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these results to study dependence of the solution of the initial…

We define Schwartz functions, tempered functions and tempered distributions on (possibly singular) real algebraic varieties. We prove that all classical properties of these spaces, defined previously on affine spaces and on Nash manifolds,…

The paper contains a new proof of the theorem by Krieger which establishes the canonicity of the future cover of a sofic shift. In addition the paper describes a method to produce new canonical covers from a given one, resulting in…

Noether's problem is classical and very important problem in algebra. It is an intrinsically interesting problem in invariant theory, but with far reaching applications in the sutdy of moduli spaces, PI-algebras, and the Inverse problem of…