Related papers: On weighted singular vectors for multiple weights

This paper concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights $w:=\exp(-Q)$ with finite moments and with smooth external fields $Q:\mathbb R\to [0,\infty)$, with varying…

We provide an explicit combinatorial description of highest weights of simple highest weight modules over the simple affine vertex algebra of type A of admissible level k. For admissible simple highest weight modules corresponding to the…

We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…

In this paper we discuss some properties of completely irrational subspaces. We prove that there exist completely irrational subspaces that are badly approximable and, moreover, sets of such subspaces are winning in different senses. We get…

We prove a sharp isoperimetric inequality for measured Finsler manifolds having non-negative Ricci curvature and Euclidean volume growth. We also prove a rigidity result for this inequality, under the additional hypotheses of boundedness of…

We prove a uniform vector-valued Wiener-Wintner Theorem for a class of operators that includes compositions of ergodic Koopman operators with contractive multiplication operators. Our results are new even in the case of complex-valued…

For a twisted affine Lie superalgebra with nonzero odd part, we study {tight irreducible weight modules} with bounded weight multiplicities and show that if the action of nonzero real vectors of each affine component of the zero part is…

We develop a theory of weights for a quantum analogue of the symmetric pair (gl4,gl2 x gl2) realised as a quantum symmetric pair subalgebra. Based on Letzter's triangular decomposition we define Verma modules. Using magical operators that…

In this paper, we study the weighted $n$-dimensional badly approximable points on manifolds. Given a $C^n$ differentiable non-degenerate submanifold $\mathcal{U} \subset \mathbb{R}^n$, we will show that any countable intersection of the…

We prove weighted $q$-variation inequalities with $2<q<\infty$ for differential and singular integral operators in higher dimensions. The vector-valued extensions of these inequalities are also given.

We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best…

We formulate Vojta's conjecture for smooth weighted projective varieties, weighted multiplier ideal sheaves, and weighted log pairs and prove that all three versions of the conjecture are equivalent. In the process, we introduce generalized…

Theorems on the existence of vector fields with given sets of Indexes of isolated Singular points are proved for the cases of closed manifolds, pairs of manifolds, manifolds with boundary, and gradient fields. It is proved that, on a…

Unbounded complex symmetric weighted shifts are studied. Complex symmetric unilateral weighted shifts whose $C^\infty$ vectors contain the image of the canonical orthonormal basis under the conjugation are shown to be decomposable into an…

We define a very general "parametric connect sum" construction which can be used to eliminate isolated conical singularities of Riemannian manifolds. We then show that various important analytic and elliptic estimates, formulated in terms…

We discuss irreducible highest weight representations of the sl(2) loop algebra and reducible indecomposable ones in association with the sl(2) loop algebra symmetry of the six-vertex model at roots of unity. We formulate an elementary…

It is expected that a totally invariant divisor of a non-isomorphic endomorphism of the complex projective space is a union of hyperplanes. In this paper, we compute an upper bound for the degree of such a divisor. As a consequence, we…

We prove that the quotient of an irreducible representation of a special unitary group of rank greater than 1 cannot be a smooth manifold.

We introduce equivariant versions of uniform rationality: given an algebraic group G, a G-variety is called G-uniformly rational (resp. G-linearly uniformly rational) if every point has a G-invariant open neighborhood equivariantly…

Let $\PP^d$ be the $d$-fold direct product of the set of primes. We prove that if $A$ is a subset of $\PP^d$ of positive relative upper density then $A$ contains infinitely many "corners", that is sets of the form $\{x,x+te_1,...,x+te_d\}$…