Related papers: Strong ultra-regularity properties for positive el…
In this paper we establish that several maximal operators of convolution type, associated to elliptic and parabolic equations, are variation-diminishing. Our study considers maximal operators on the Euclidean space $\mathbb{R}^d$, on the…
We construct an effective field theory for fusion of conformal defects of any codimension in $d\geq 3$ conformal field theories. We fully solve the constraints of Weyl invariance for defects of arbitrary shape on general curved bulk…
In this paper, we investigate the relationship between positive definite functions on the unit sphere $\sph$ and on the Euclidean space $\RR^d$. For the dimension $d$ to be odd, a new technique is developed to establish the inheritance of…
Let $(X,\mathcal{B},m,\tau)$ be a dynamical system with $\ds (X,\mathcal{B},m)$ a probability space and $\ds \tau$ an invertible, measure preserving transformation. The present paper deals with the almost everywhere convergence in…
We consider a quantum group interpretation of the non-anticommutative deformations in Euclidean supersymmetric theories. Twist deformations in the corresponding superspaces and Lie superalgebras are constructed in terms of the left…
The Weak Gravity Conjecture has recently been re-formulated in terms of a particle with non-negative self-binding energy. Because of the dual conformal field theory (CFT) formulation in the anti-de Sitter space the conformal dimension…
Let $T(X)$ (resp. L(V)) be the semigroup of all transformations (resp. linear transformations) of a set $X$ (resp. vector space $V$). For a subset $Y$ of $X$ and a subsemigroup $\mathbb{S}(Y)$ of $T(Y)$, consider the subsemigroup…
We define categories $\mathcal{O}^w$ of representations of Borel subalgebras $\mathcal{U}_q\mathfrak{b}$ of quantum affine algebras $\mathcal{U}_q\hat{\mathfrak{g}}$, which come from the category $\mathcal{O}$ twisted by Weyl group elements…
We consider quite general differential operators on the circle with a small random lower order perturbation. We embrace two points a view, the semiclassical and the high energy limits. We show (a) in the semiclassical limit, that the…
We prove that the Deligne-Lusztig varieties associated to elements of the Weyl group which are of minimal length in their twisted class are affine. Our proof differs from the proof of He and Orlik-Rapoport and it is inspired by the case of…
Recently, two new topological properties for operators acting on a topological vector space were introduced: strong hypercyclicity and hypermixing. We introduce a new property called ultra hypercyclicity and compare it to strong…
Initially motivated by Hrushovski's paper on definability patterns, we obtain homeomorphisms between Ellis semigroups related to natural actions of the automorphism groups of first order structures and certain collections of types and…
For an increasing sequence $(T_n)$ of one-parameter semigroups of sub Markovian kernel operators over a Polish space, we study the limit semigroup and prove sufficient conditions for it to be strongly Feller. In particular, we show that the…
This paper, together with Part II, expands the results of math.DG/9803051. In Part I we study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective…
We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…
It is shown that the equations of motion of eleven-dimensional supergravity follow from setting the dimension zero components of the superspace torsion tensor equal to the Dirac matrices. The proof of this assertion is facilitated by the…
In this paper we define the so-called twisted Heisenberg superalgebras over the complex number field by adding derivations to Heisenberg superalgebras. We classify the fine gradings up to equivalence on twisted Heisenberg superalgebras and…
Using the Moyal *-product and orthosymplectic supersymmetry, we construct a natural non trivial supertrace and an associated non degenerate invariant supersymmetric bilinear form for the Lie superalgebra structure of the Weyl algebra. We…
We consider the convex set of ( unital ) positive ( completely ) maps from a $C^*$ algebra $\cla$ to a von-Neumann sub-algebra $\clm$ of $\clb(\clh)$, the algebra of bounded linear operators on a Hilbert space $\clh$ and study its extreme…
We construct a normal form suited to {\it fast driven systems}. We call so systems including actions ${\rm I}$, angles {$\psi$}, and one fast coordinate $y$, moving under the action of a vector--field $N$ depending only on ${\rm I}$ and $y$…