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Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations

Boaz Tsaban, Lubomyr Zdomsky (2012)

Journal of the European Mathematical Society

A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces X which have the Hurewicz property hereditarily. We proceed to consider the class of Arhangel’skii α 1 spaces, for which every sheaf at a point can be amalgamated in a natural way. Let C p ( X ) denote the space of continuous real-valued functions on X with the topology of pointwise convergence. Our main result...

Hessian determinants as elements of dual Sobolev spaces

Teresa Radice (2014)

Studia Mathematica

In this short note we present new integral formulas for the Hessian determinant. We use them for new definitions of Hessian under minimal regularity assumptions. The Hessian becomes a continuous linear functional on a Sobolev space.

Hidden structures in the class of convex functions and a new duality transform

Shiri Artstein-Avidan, Vitali Milman (2011)

Journal of the European Mathematical Society

Our main intention in this paper is to demonstrate how some seemingly purely geometric notions can be presented and understood in an analytic language of inequalities and then, with this understanding, can be defined for classes of functions and reveal new and hidden structures in these classes. One main example which we discovered is a new duality transform for convex non-negative functions on n attaining the value 0 at the origin (which we call “geometric convex functions”). This transform, together...

Hilbert inequality for vector valued functions

Namita Das, Srinibas Sahoo (2011)

Archivum Mathematicum

In this paper we consider a class of Hankel operators with operator valued symbols on the Hardy space Ξ 2 ( 𝕋 ) where Ξ is a separable infinite dimensional Hilbert space and showed that these operators are unitarily equivalent to a class of integral operators in L 2 ( 0 , ) Ξ . We then obtained a generalization of Hilbert inequality for vector valued functions. In the continuous case the corresponding integral operator has matrix valued kernels and in the discrete case the sum involves inner product of vectors in the...

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