相关论文: Yet another inverse function theorem

We consider the classical Inverse Function Theorem of Nash and Moser from the angle of some recent development by Ekeland and the authors. Geometrisation of tame estimates coupled with certain ideas coming from Variational Analysis when…

We prove an inverse function theorem of Nash-Moser type for maps between Fr\'echet spaces satisfying tame estimates. In contrast to earlier proofs, we do not use the Newton method, that is, we do not use quadratic convergence to overcome…

I present an inverse function theorem for differentiable maps between Frechet spaces which contains the classical theorem of Nash and Moser as a particular case. In contrast to the latter, the proof does not rely on the Newton iteration…

The aim of this article is to present the category of bounded Frechet manifolds in respect to which we will review the geometry of Frechet manifolds with a stronger accent on its metric aspect. An inverse function theorem in the sense of…

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…

In this paper we prove a local surjection theorem with continuous right-inverse for maps between Banach spaces, and we apply it to a class of inversion problems with loss of derivatives.

In this paper we prove an inverse function theorem in derived differential geometry. More concretely, we show that a morphism of curved $L_\infty$ spaces which is a quasi-isomorphism at a point has a local homotopy inverse. This theorem…

By an example we show that Olaf Mueller's assertion about his new theorems being able to give anew some classical results previously obtained via applications of Nash--Moser type theorems is unfounded. We also give another example…

We prove surjectivity result in Fr\'echet spaces of Nash-Moser type. That is, with uniform estimates over all semimorms. Our method works for functions which are only continuous and G\^ateaux differentiable like in the recent result of…

In weighted Orlicz type spaces ${\mathcal S}_{_{\scriptstyle \mathbf p,\,\mu}}$ with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of…

In terms of the best approximations of functions and generalized moduli of smoothness, direct and inverse approximation theorems are proved for Besicovitch almost periodic functions whose Fourier exponent sequences have a single limit point…

We prove an abstract Nash-Moser implicit function theorem which, when applied to control and Cauchy problems for PDEs in Sobolev class, is sharp in terms of the loss of regularity of the solution of the problem with respect to the data. The…

In the Orlicz type spaces ${\mathcal S}_{M}$, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of…

In Musilak-Orlicz type spaces ${\mathcal S}_{\bf M}$, direct and inverse approximation theorems are obtained in terms of the best approximations of functions and generalized moduli of smoothness. The question of the exact constants in…

In this paper, we present some implicit function theorems for set-valued mappings between Fr\'echet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence…

In this paper we introduce a new algorithm for solving perturbed nonlinear functional equations which admit a right-invertible linearization, but with an inverse that loses derivatives and may blow up when the perturbation parameter…

This article provides a version of scale calculus geared towards a notion of (nonlinear) Fredholm maps between certain types of Frechet spaces, retaining as many as possible of the properties Fredholm maps between Banach spaces enjoy, and…

In the seventies', Zehnder found a Nash-Moser type implicit function theorem in the analytic set-up. This theorem has found many applications in dynamical systems although its applications require, as a general rule, some efforts. We…

We prove an inversion theorem for the Fourier transform defined for normal functions, in the case when such functions are of moderate decrease, and in dimensions 2 and 3. This improves on Carleson's general almost everywhere convergence…

We prove a novel inversion theorem for functionals given as power series in infinite-dimensional spaces and apply it to the inversion of the density-activity relation for inhomogeneous systems. This provides a rigorous framework to prove…