Hyperbolic L Multipliers are Translations
نویسندگان
چکیده
The associated evolution operators which map u(0, ·) to u(t, ·) is the family of Fourier multipliers e, e := F e F . (2) Our main result shows that boundedness in L for p 6= 2 is very rare. The evolution operator is L bounded if and only if it consists of simple translations. If the multiplier (2) is an L multiplier then it is an L multiplier for the dual index, p+q = 1. By interpolation it is an L multiplier so ∃C, ∀ξ ∈ R, ∥ ∥e ∥
منابع مشابه
Isometrically Self-dual Cyclic Codes
General isometries of cyclic codes, including multipliers and translations, are introduced; and isometrically self-dual cyclic codes are defined. In terms of Type-I duadic splittings given by multipliers and translations, a necessary and sufficient condition for the existence of isometrically selfdual cyclic codes is obtained. A program to construct isometrically selfdual cyclic codes is provid...
متن کاملSome Applications of Large Sieve in Riemann Surfaces
1. Introduction. In [Ch] we gave some large sieve type inequalities involving elements of harmonic analysis in Riemann surfaces and compact Riemannian manifolds. In this paper we present some of their applications. Our results are related to the hyperbolic circle problem, which is a generalization of the classical circle problem. The latter can be formulated as counting the images of a point in...
متن کاملSpectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+
We study the spectrum of multipliers (bounded operators commuting with the shift operator S) on a Banach space E of sequences on Z. Given a multiplier M , we prove that f M(σ(S)) ⊂ σ(M) where f M is the symbol of M . We obtain a similar result for the spectrum of an operator commuting with the shift on a Banach space of sequences on Z. We generalize the results for multipliers on Banach spaces ...
متن کاملMagnetic Translations in Hyperbolic Geometry
We study random walks on the three-strand braid group B3, and in particular compute the drift, or average topological complexity of a random braid, as well as the probability of trivial entanglement. These results involve the study of magnetic random walks on hyperbolic graphs (hyperbolic Harper-Hofstadter problem), what enables to build a faithful representation of B3 as generalized magnetic t...
متن کامل