Related papers: Anisotropic Holder and Sobolev spaces for hyperbol…

Given $f:\partial (-1,1)^n\to{\mathbb R}$, consider its radial extension $Tf(X):=f(X/\|X\|_{\infty})$, $\forall\, X\in [-1,1]^n\setminus\{0\}$. In "On some questions of topology for $S^1$-valued fractional Sobolev spaces" (RACSAM 2001), the…

We consider a normal operator $T$ on a Hilbert space $H$. Under various assumptions on the spectrum of $T$, we give bounds for the spectrum of $T+A$ where $A$ is $T$-bounded with relative bound less than 1 but we do not assume that $A$ is…

We introduce Besov and Triebel--Lizorkin spaces on a manifold with boundary adapted to H\"ormander vector fields, near a so-called non-characteristic point of the boundary. We prove sharp results in these spaces for the corresponding…

We study the problem of an appropriate choice of derivatives associated with discrete Fourier-Bessel expansions. We introduce a new so-called essential measure Fourier-Bessel setting, where the relevant derivative is simply the ordinary…

We derive sharp bounds for three types of eigenvalue problems. First, we derive an upper bound for the first $p$-Dirichlet eigenvalue on conformally compact (CC) spaces. As a consequence, we show that for a class of CC submanifolds of…

We consider Banach spaces equipped with a set of strongly continuous bounded semigroups satisfying certain conditions. Using these semigroups we introduce an analog of a modulus of continuity and define analogs of Besov norms. A…

Coning off a collection of uniformly quasiconvex subsets of a Gromov hyperbolic space leaves a new space, called the cone-off. Kapovich and Rafi generalized work of Bowditch to show this space is still Gromov hyperbolic. We show that the…

The spectral properties of non-self-adjoint extensions $A_{[B]}$ of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions. These extensions are given in…

Let $T$ be a quasinilpotent operator on a Banach space. Under assumptions of a certain nonsymmetry in the growth of the resolvent of $T$, it is proved that every operator in the commutant of $T$ is not unicellular. In particular, $T$ has…

The aim of this paper is to establish well-posedness properties for hyperbolic PDEs on Fourier Lebesgue spaces. We consider hyperbolic operators with complex characteristics. Since our approach comes from harmonic analysis, we establish…

Some preliminaries and basic facts regarding unbounded Wiener-Hopf operators (WH) are provided. WH with rational symbols are studied in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency…

We prove results on complex interpolation of vector-valued Sobolev spaces over the half-line with Dirichlet boundary condition. Motivated by applications in evolution equations, the results are presented for Banach space-valued Sobolev…

Calculating the spectral invariant of Floer homology of the distance function, we can find some kind of superheavy subsets in symplectic manifolds. We show if convex open subsets in Euclidian space with the standard symplectic form are…

A complete description of resonances for rational toral Anosov diffeomorphisms preserving certain Reinhardt domains is presented. As a consequence it is shown that every homotopy class of two-dimensional Anosov diffeomorphisms contains maps…

Let M be a closed orientable irreducible 3-manifold, and let f be a diffeomorphism over M. We call an embedded 2-torus T an Anosov torus if it is invariant and the induced action of f over \pi_1(T) is hyperbolic. We prove that only few…

In this paper, we consider pseudodifferential operators on the torus with operator-valued symbols and prove continuity properties on vector-valued toroidal Besov spaces, without assumptions on the underlying Banach spaces. The symbols are…

Let $M$ be a closed 3-manifold which admits an Anosov flow. In this paper we develop a technique for constructing partially hyperbolic representatives in many mapping classes of $M$. We apply this technique both in the setting of geodesic…

We study the solutions of equations of type $f(D,\alpha)u=v$, where $f(D,\alpha)$ is a $p$-adic pseudo-differential operator. If $v$ is a Bruhat-Schwartz function, then there exists a distribution $E_{\alpha}$, a fundamental solution, such…

We consider a $\mathbb R/\mathbb Z$ extension of an Anosov diffemorphism of a compact Riemannian manifold by a random function $\tau$ and show that the flat traces of the transfer operator, reduced with respect to frequency in the fibers,…

The theorem on the existence of maximal nonnegative invariant subspaces for a special class of dissipative operators in Hilbert space with indefinite inner product is proved in the paper. It is shown in addition that the spectra of the…