Related papers: On the Range Characterization of the two dimension…
We introduce the notion of a two-scale branching function associated with an arbitrary metric space, which encodes the lower and upper box dimensions as well as the Assouad spectrum. If the metric space is quasi-doubling, this function is…
We consider vector fields $X$ on a closed manifold $M$ with rest points of Morse type. For such vector fields we define the property of exponential growth. A cohomology class $\xi\in H^1(M;\mathbb R)$ which is Lyapunov for $X$ defines…
In a previous paper, we presented an Abstract Beurling's Theorem for valuation Hilbert modules over valuation algebras. In this paper, we shall apply this theorem to obtain complete descriptions of the closed invariant subspaces of a number…
We propose a harmonic superspace description of the non-linear vector-tensor N=2 multiplet. We show that there exist two inequivalent version: the old one in which one of the vectors is the field-strength of a gauge two-form, and a new one…
The study of the packing of a length of wire in a two dimensional domain is done using techniques of conformal maps. The resulting scaling properties are derived through the Coulomb gas formalism of Conformal Field Theories. An analogy is…
The two weight inequality for the Hilbert transform arises in the settings of analytic function spaces, operator theory, and spectral theory, and what would be most useful is a characterization in the simplest real-variable terms. We show…
Consider a measurable space with an atomless finite vector measure. This measure defines a mapping of the $\sigma$-field into an Euclidean space. According to the Lyapunov convexity theorem, the range of this mapping is a convex compactum.…
Different (not only by sign) affine connections are introduced for contravariant and covariant tensor fields over a differentiable manifold by means of a non-canonical contraction operator, defining the notion dual bases and commuting with…
We derive weighted versions of the Cwikel-Lieb-Rozenblum inequality for the Schr\"odinger operator in two dimensions with a nontrivial Aharonov-Bohm magnetic field. Our bounds capture the optimal dependence on the flux and we identify a…
Determining range, Doppler and astrometric observables is of crucial interest for modelling and analyzing space observations. We recall how these observables can be computed when the travel time of a light ray is known as a function of the…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…
Measuring the photon energy spectrum in radiative B decays provides essential help for gaining theoretical control over semileptonic B transitions. The hadronic recoil mass distribution in B -> X_u \ell\nu promises the best environment for…
We prove the $L^p (p > 3/2)$ boundedness of the directional Hilbert transform in the plane relative to measurable vector fields which are constant on suitable Lipschitz curves.
The momentum ray transform $I^k$ integrates a rank $m$ symmetric tensor field $f$ over lines of ${\R}^n$ with the weight $t^k$: $ (I^k\!f)(x,\xi)=\int_{-\infty}^\infty t^k\l f(x+t\xi),\xi^m\r\,dt. $ We give the range characterization for…
For a very ample line bundle L on a compact connected complex manifold X, with a real structure, we discuss entanglement properties of certain sequences of vectors in tensor products of spaces of holomorphic sections of powers of L.
We prove variable coefficient versions of L^p boundedness results on Hilbert transforms and maximal functions along convex curves in the plane.
We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we…
The main result is the identification of the orthogonal complement of the subalgebra of conformal vector field inside the algebra of all vector fields of a compact flat 2-manifold. As a fundamental tool, the complete Hodge decomposition for…
We use the arithmetic-combinatorial method of Katz and Tao to give mixed-norm estimates for the x-ray transform on R^d when d \geq 4. As an application, we obtain an improved estimate for the Hausdorff dimension of (d,k) sets, which are…
We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible $\zed$-valued…