Related papers: Unique continuation results for certain generalize…

We study maximal monotone operators $A : X \rightrightarrows X^*$ whose Fitzpatrick family reduces to a singleton; such operators will be called uniquely representable. We show that every such operator is cyclically monotone (hence,…

We generalise the analysis in [arXiv:0904.1744] to superspace, and explicitly prove that for any embedding of surface operators in a general, twisted N=2 pure abelian theory on an arbitrary four-manifold, the parameters transform naturally…

We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The…

A wide and natural class of closed currents - which are differences of positive closed currents - can be constructed by pulling back smooth closed forms using rational maps. These currents are very singular in general, and hence defining…

Let $M$ be the space of real $n\times m$ matrices which can be identified with the Euclidean space $R^{nm}$. We introduce continuous wavelet transforms on $M$ with a multivalued scaling parameter represented by a positive definite symmetric…

We study the spectral properties of discrete one-dimensional Schr\"odinger operators with Sturmian potentials. It is shown that the point spectrum is always empty. Moreover, for rotation numbers with bounded density, we establish purely…

The continuity property in the Sobolev space $W^{k,p}({\bf R}^m)$ of wave operators of scattering theory for $m$-dimensional single-body Schr\"odinger operator is considered when the resolvent of the operator has singularities at the bottom…

The simplest and most natural examples of completely nonunitary contractions on separable complex Hilbert spaces which have polynomial characteristic functions are the nilpotent operators. The main purpose of this paper is to prove the…

Consider the differential operator H = -(1/m(x))L, where L is the N-dimensional Laplacian, in the weighted Hilbert space of square integrable functions on N-dimensional Euclidean space with weight m(x)dx. Here m(x) is a positive step…

The momentum ray transform $I^k$ integrates a rank $m$ symmetric tensor field $f$ over lines with the weight $t^k$: $ (I^k\!f)(x,\xi)=\int_{-\infty}^\infty t^k\langle f(x+t\xi),\xi^m\rangle\,dt. $ In particular, the ray transform $I=I^0$…

We give the complete list of all first-order consistent interaction vertices for a set of exterior form gauge fields of form degree >1, described in the free limit by the standard Maxwell-like action. A special attention is paid to the…

Let $\mathfrak{m}$ be a random tessellation in $\mathbf{R}^d$ observed in a bounded Borel subset $W$ and $f(\cdot)$ be a measurable function defined on the set of convex bodies. To each cell $C$ of $\mathfrak{m}$ we associate a point $z(C)$…

We discuss the possibility to construct an effective quantum field theory for an axial vector coupled to a Dirac spinor field. A massive axial vector describes antisymmetric torsion. The consistency conditions include unitarity and…

The classical Weyl-von Neumann theorem states that for any self-adjoint operator $A$ in a separable Hilbert space $\mathfrak H$ there exists a (non-unique) Hilbert-Schmidt operator $C = C^*$ such that the perturbed operator $A+C$ has purely…

It is postulated in general relativity that the matter energy-momentum tensor (named the stress tensor) vanishes if and only if all the matter fields vanish. In classical lagrangian field theory the stres tensor is the variational…

A necessary condition for partial breaking of N=2 global supersymmetry is the presence of nonlinear deformations of the field transformations which cannot be generated by background values of auxiliary fields. This work studies the simplest…

This paper has three objectives. First to recall the link between the classical Legendre-Fenschel transformation and a useful isomorphism between 1-jets of functions on a vector bundle and on its dual. As a particular consequence we obtain…

For every $n>0$ there is a unitary operator $U$ such that the unitary operator with simple Lebesgue spectrum is isomorphic to the tensor product $U\otimes U^2\otimes\dots\otimes U^{2^n}.$ There is an ergodic automorphism $T$ with its…

Let $\gH$ be a Hilbert space and let $A$ be a simple symmetric operator in $\gH$ with equal deficiency indices $d:=n_\pm(A)<\infty$. We show that if, for all $\l$ in an open interval $I\subset\bR$, the dimension of defect subspaces…

We prove in this paper the weak consistency of a general finite volume convection operator acting on discrete functions which are possibly not piecewise-constant over the cells of the mesh and over the time steps. It yields an extension of…