Continuity of the fundamental operations on distributions having a specified wave front set (with a counter example by Semyon Alesker)
نویسندگان
چکیده
The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front set satisfies some conditions. Thus, it is natural to investigate the topological properties of these operations between spaces D′ Γ of distributions having a wave front set included in a given closed cone Γ of the cotangent space. As discovered by S. Alesker, the pull-back is not continuous for the usual topology on D′ Γ, and the tensor product is not separately continuous. In this paper, a new topology is defined for which the pull-back and push-forward are continuous, the tensor 2010 Mathematics Subject Classification: Primary 46F10; Secondary 35A18.
منابع مشابه
0 Ju l 2 00 7 Plurisubharmonic functions on the octonionic plane and Spin ( 9 ) - invariant valuations on convex sets
A new class of plurisubharmonic functions on the octonionic plane O2 ≃ R16 is introduced. An octonionic version of theorems of A.D. Aleksandrov [3] and ChernLevine-Nirenberg [24], and B locki [21] are proved. These results are used to construct new examples of continuous translation invariant valuations on convex subsets of O2 ≃ R 16. In particular a new example of Spin(9)-invariant valuation o...
متن کامل1 Se p 20 06 Quaternionic plurisubharmonic functions and their applications to convexity
The goal of this article is to present a survey of the recent theory of plurisubharmonic functions of quaternionic variables, and its applications to theory of valuations on convex sets and HKT-geometry (HyperKähler with Torsion). The exposition follows the articles [4], [5], [7] by the author and [8] by M. Verbitsky and the author.
متن کاملAlgebraic Structures on Valuations, Their Properties and Applications
We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincaré duality and hard Lefschetz theorem), and their relations and applications to integral geometry. 2000 Mathematics Subject Classification: 46, 47.
متن کاملPlurisubharmonic functions on the octonionic plane and Spin ( 9 ) - invariant valuations on convex sets
A new class of plurisubharmonic functions on the octonionic plane O2 ≃ R16 is introduced. An octonionic version of theorems of A.D. Aleksandrov [3] and ChernLevine-Nirenberg [24], and B locki [21] are proved. These results are used to construct new examples of continuous translation invariant valuations on convex subsets of O2 ≃ R 16. In particular a new example of Spin(9)-invariant valuation o...
متن کامل2 9 Ju n 20 06 Quaternionic plurisubharmonic functions and their applications to convexity
The goal of this article is to present a survey of the recent theory of plurisubharmonic functions of quaternionic variables, and its applications to theory of valuations on convex sets and HKT-geometry (HyperKähler with Torsion). The exposition follows the articles [4], [5], [7] by the author and [8] by M. Verbitsky and the author.
متن کامل