Related papers: A local Levinson theorem for compact symmetric spa…

For a finite and positive measure space $(\Omega,\Sigma,\mu)$ and any weakly compact convex subset of $L\sp\infty(\Omega,\Sigma,mu)$, a fixed point theorem for a class of nonexpansive self-mappings is proved. An analogous result is obtained…

In this work one proves that, around each point of a dense open set (regular points), a real analytic or holomorphic bihamiltonian structure decomposes into a product of a Kronecker bihamiltonian structure and a symplectic one if a…

In this short note, we prove the non-existence of slow and fast small nontrivial compact solutions for the Euler-Poisson system in $1$D. The proof is based on the virial estimate which provides local in space average decay of bounded small…

In this paper we discuss function spaces on a general noncompact Lie group, namely the scales of Triebel--Lizorkin and Besov spaces, defined in terms of a sub-Laplacian with drift. The sub-Laplacian is written as negative the sum of squares…

The n-dimensional Lorentzian manifolds with vanishing second covariant derivative of the Riemann tensor (2-symmetric spacetimes) are characterized and classified. The main result is that either they are locally symmetric or they have a…

We prove that any topological loop homeomorphic to a sphere or to a real projective space and having a compact-free Lie group as the inner mapping group is homeomorphic to the circle. Moreover, we classify the differentiable $1$-dimensional…

The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of…

We prove that E. De Giorgi's conjecture for the nonlocal approximation of free-discontinuity problems extends to the case of functionals defined in terms of the symmetric gradient of the admissible field. After introducing a suitable class…

We prove various results connecting structural or algebraic properties of graphs and groups to conditions on their spaces of harmonic functions. In particular: we show that a group with a finitely supported symmetric measure has a…

We give necessary conditions for the existence of a compact manifold locally modelled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and…

All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and we display the corresponding metrics in local coordinates.…

Given a charge and current distribution with compact support, the associated potentials and fields are generally not integrable in the classical sense. However, it is convenient to be able to define their Fourier transform in order to…

We prove a Wiener-Tauberian theorem for $L^1$-spherical functions on a semisimple Lie group of arbitrary real rank. We also establish a Schwartz theorem for complex groups. As a corollary we obtain a Wiener-Tauberian type theorem for for…

Regularity of the transform of Laplace in the opened area of 0 is proved with help of some methods of the transform of Fourier. The class of the transform of Laplace from the transform of Fourier is considered from some functions without a…

We provide a functional Rogers-Shephard type inequality for log-concave functions on $\mathbb R^n$ and any $1$-reducible $s$-cover of $[n]$. As a consequence, we derive a sharp local Liakopoulos-Meyer type inequality for $n$-dimensional…

We note a generalization of Whyte's geometric solution to the von Neumann problem for locally compact groups in terms of Borel and clopen piecewise translations. This strengthens a result of Paterson on the existence of Borel paradoxical…

We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifolds, based on Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a…

We extend to infinite dimensional Hilbert spaces a celebrated result, due to B. Polyak, about the convexity of the joint image of quadratic functions. We give sufficient conditions which assure that the joint image is also closed. However,…

It is a classical theorem that if a function is integrable along the boundary of the unit circle, then the function is the nontangential limit of a holomorphic function on the open disc if and only if its Fourier coefficients for…

We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is…