— In this paper we define Banach spaces of overconvergent half-integral weight p-adic modular forms and Banach modules of families of overconvergent halfintegral weight p-adic modular forms over admissible open subsets of weight space. Both spaces are equipped with a continuous Hecke action for which U p2 is moreover compact. The modules of families of forms are used to construct an eigencurve ...

— In this paper we define Banach spaces of overconvergent half-integral weight p-adic modular forms and Banach modules of families of overconvergent halfintegral weight p-adic modular forms over admissible open subsets of weight space. Both spaces are equipped with a continuous Hecke action for which Up2 is moreover compact. The modules of families of forms are used to construct an eigencurve p...

Abstract In this short note, we will study the existence of a vector space continuous functions $$f:{\mathbb {Z}}_p\rightarrow \mathbb Q_p$$ f : Z p → Q , where $${\mathbb {Z}}_p$...

The shearlet representation has gained increasingly more prominence in recent years as a flexible mathematical framework which enables the efficient analysis of anisotropic phenomena by combining multiscale analysis with the ability to handle directional information. In this paper, we introduce a class of shearlet smoothness spaces which is derived from the theory of decomposition spaces recent...

Roughly speaking, the semialgebraic cell decomposition theorem for p-adic numbers describes piecewise the p-adic valuation of p-adic polyno-mials (and more generally of semialgebraic p-adic functions), the pieces being geometrically simple sets, called cells. In this paper we prove a similar cell decomposition theorem to describe piecewise the valuation of analytic functions (and more generally...