Related papers: The Heyde Theorem on a-adic Solenoids

A proof is given of Rosenthal's \(\ell_1\) theorem.

A measured solenoid is a compact laminated space endowed with a transversal measure. The De Rham $L^2$-cohomology of the solenoid is defined by using differential forms which are smooth in the leafwise directions and $L^2$ in the…

We prove the $\boldsymbol{p}$-adic duality theorem for the finite star-multiple polylogarithms. That is a generalization of Hoffman's duality theorem for the finite multiple zeta-star values.

A basic family of solenoids is discussed, especially from the point of view of analysis on metric spaces.

We give a relatively easy proof of the Erd\H os-Kac theorem via computing moments. We show how this proof extends naturally in a sieve theory context, and how it leads to several related results in the literature.

Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.

We prove analogues of the Craig interpolation theorem for the continuous model theory of metric structures.

We give sufficient conditions for the existence of a model structure on operads in an arbitrary symmetric monoidal model category. General invariance properties for homotopy algebras over operads are deduced.

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

As a corollary of nonabelian Hodge theory, Simpson proved a strong Lefschetz theorem for complex polarized variations of Hodge structure. We show an arithmetic analog. Our primary technique is $p$-adic nonabelian Hodge theory. Conditional…

Heyde proved that a Gaussian distribution on a real line is characterized by the symmetry of the conditional distribution of one linear form given another. The present article is devoted to an analog of the Heyde theorem in the case when…

The analogue of Goldie's Theorem for prime rings is proved for rings graded by abelian groups, eliminating unnecessary additional hypotheses used in earlier versions.

We give a new proof of Ohta's Lambda-adic Eichler-Shimura isomorphism using p-adic Hodge theory and the results of Bloch-Kato and Hyodo on p-adic etale cohomology.

In this paper, we proved a rigidity theorem of the Hodge metric for concave horizontal slices and a local rigidity theorem for the monodromy representation.

Based on the strong analogy between the category of log mixed Hodge structures and the category ${\cal A}_X$ of $\ell$-adic nature, which we have introduced in the previous part and is closely related to the weight-monodromy conjecture, we…

We prove a version of Dedekind's Transposition Principle that holds in lattices of equivalence relations.

We prove an analogue of the Centralizer Theorem in the context of Artin-Tits groups.

We prove a homotopy theorem for sheaves. Its application shortens and simplifies the proof of many Oka principles such as Gromov's Oka principle for elliptic submersions.

We give a short proof of Ahlfors' theorem on covering surfaces.

In this note we give a detailed proof of a theorem of Aubin.