Relative difference property

Relative Kazhdan Property

We perform a systematic investigation of Kazhdan’s relative Property (T) for pairs (G,X), G a locally compact group and X any subset. When G is a connected Lie group or a p-adic algebraic group, we provide an explicit characterization of subsets X ⊂ G such that (G,X) has relative Property (T). In order to extend this characterization to lattices Γ ⊂ G, a notion of “resolutions” is introduced, a...

Property and Relative Status

Property does many things-it incentivizes productive activity, facilitates exchange, forms an integral part of individual identity, and shapes communities. But property does something equally fundamental: it communicates. And perhaps the most ubiquitous and important messages that property communicates have to do with relative status, with the material world defining and reinforcing a variety o...

A Difference Property for Polynomials

Weak difference property of functions with the Baire property

We prove that the class of functions with the Baire property has the weak difference property in category sense. That is, every function for which f(x+h)−f(x) has the Baire property for every h ∈ R can be written in the form f = g+H+φ where g has the Baire property, H is additive, and for every h ∈ R we have φ(x+h)−φ(x) 6= 0 only on a meager set. We also discuss the weak difference property of ...

Relative invariants , difference equations , and

Acknowledgements First of all I would like to thank my supervisor Professor T. Kimura. He taught me how to learn mathematics from the beginning when I just started afresh my life. About four years ago he suggested to study on archimedean local zeta functions of several variables as my first research task for the Master's thesis. I can not give enough thanks to his heartwarming encouragement all...