Related papers: A converse extrapolation theorem for translation i…

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 give a new simpler proof of a theorem of Jayne and Rogers.

We give a general formulation of Jensen's operator inequality for unital fields of positive linear mappings, and we consider different types of converse inequalities.

In this short note we give counterexamples to several results related to extension theorems published recently.

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…

We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.

In this paper we develop the theory of quantum reverse hypercontractivity inequalities and show how they can be derived from log-Sobolev inequalities. Next we prove a generalization of the Stroock-Varopoulos inequality in the…

We give an example of non-translation invariant product measure obtained from two translation invariant measures, one of which is non-sigma finite. This particular example also suggests that there can be infinitely many product measures if…

We prove a T(1) theorem for bilinear singular integral operators (trilinear forms) with a one-dimensional modulation symmetry.

We propose a new interpretation of doubly special relativity based on the distinction between the momenta and the translation generators in its phase space realization. We also argue that the implementation of the theory does not…

We study the dynamics of the renormalization operator for multimodal maps. In particular, we prove the exponential convergence of this operator for infinitely renormalizable maps with same bounded combinatorial type.

In this current article, we introduce the quadruple Shehu transform and its inverse. We also introduce some properties of quadruple Shehu transform. The Convolution theorem and its proof are also discussed. Further, to solve homogeneous and…

We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…

We study naturality properties of the transverse invariant in knot Floer homology under contact (+1)-surgery. This can be used as a calculational tool for the transverse invariant. As a consequence, we show that the Eliashberg-Chekanov…

We formulate and prove a version of the celebrated Coifman-Rochberg-Weiss commutator theorem for the real method of interpolation

We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.

In this paper, we prove the Mohebi-Radjabalipour Conjecture under a little additional condition, and obtain a new invariant subspace theorem for subdecomposable operators. Our main results contain known results in this topic as special…

We give alternative proofs to certain results in the paper "Weak limits of almost invariant projections" by using ultraproducts of operators.

We construct filtrations on homotopy invariant sheaves with transfers and show that under Ayoub's conjectures on $n$-motives, our filtration agrees with the one conjectured by Ayoub and Barbieri-Viale if the latter exists. Our construction…

By nonstandard analysis, a very short and elementary proof of the Spectral Theorem for unbounded self-adjoint operators is given.