Related papers: Functionally $\sigma$-discrete mappings and a gene…
We generalize the Lebesgue-Hausdorff Theorem on the characterization of Baire-one functions for $\sigma$-strongly functionally discrete mappings defined on arbitrary topological spaces
We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not necessarily locally convex) topological…
We provide sufficient conditions for the existence of a strong derivable map and calculate its derivative by employing a result in our previous work on strong derivability of maps arising by functional calculus of an unbounded scalar type…
On a reflexive Banach space $X$, if an operator $T$ admits a functional calculus for the absolutely continuous functions on its spectrum $\sigma(T) \subseteq \mathbb{R}$, then this functional calculus can always be extended to include all…
We prove a generalized implicit function theorem for Banach spaces, without the usual assumption that the subspaces involved being complemented. Then we apply it to the problem of parametrization of fibers of differentiable maps, the Lie…
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
We prove that if $X$ is a paracompact space, $Y$ is a metric space and $f:X\to Y$ is a functionally fragmented map, then (i) $f$ is $\sigma$-discrete and functionally $F_\sigma$-measurable; (ii) $f$ is a Baire-one function, if $Y$ is weak…
We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all…
We describe a closed operator functional calculus in Banach modules over the group algebra $L^1(\mathbb R)$ and illustrate its usefulness with a few applications. In particular, we deduce a spectral mapping theorem for operators in the…
We construct two bounded functional calculi for sectorial operators on Banach spaces, which enhance the functional calculus for analytic Besov functions, by extending the class of functions, generalizing and sharpening estimates, and…
We introduce a sheaf theoretic viewpoint on functional analysis designed for infinite dimensional Lie group actions. We develop functional calculus for Banach valued functors and, in particular, prove the existence of an exponential map for…
We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test…
Let $G$ be a connected reductive group over a $p$-adic field $F$ of characteristic 0 and let $M$ be an $F$-Levi subgroup of $G.$ Given a discrete series representation $\sigma$ of $M(F),$ we prove that there exists a locally constant and…
Usually, for extension of local maps, one uses multiplication by so called bump functions. However, majority of infinite-dimensional linear topological spaces do not have smooth bump functions. Therefore, in \cite{BR} we suggested a new…
We prove an implicit function theorem for functions on infinite-dimensional Banach manifolds, invariant under the (local) action of a finite dimensional Lie group. Motivated by some geometric variational problems, we consider group actions…
This article is centered around generalizing a previous implicit function theorem of the author to be applicable for maps f:E sqcap F to F which can be lifted to Keller C^k_pi maps f_i:E sqcap F_i to F_i with F_i Banach and F=projlim F_i .…
Given a Banach algebra $ \mathcal{A} $ and a continuous homomorphism $\sigma$ on it, the notion of $\sigma$-biflatness for $ \mathcal{A} $ is introduced. This is a generalization of biflatness and it is shown that they are distinct. The…
It is known that the classical Banach--Stone theorem does not extend to the class of $AC(\sigma)$ spaces of absolutely continuous functions defined on compact subsets of the complex plane. On the other hand, if $\sigma$ is restricted to the…
We study the existence of global implicit functions for equations defined on open subsets of Banach spaces. The partial derivative with respect to the second variable is only required to have a left inverse instead of being invertible.…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…