18 research outputs found
A contractive Hardy-Littlewood inequality
We prove a contractive Hardy-Littlewood type inequality for functions from
, which is sharp in the first two Taylor
coefficients and asymptotically at infinity.Comment: 8 page
Contractive projections in Paley-Wiener spaces
Let and be disjoint finite unions of parallelepipeds. We describe
necessary and sufficient conditions on the sets and exponents
such that the canonical projection from to
is a contraction
Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials
Let be a subset of . We show that if has
`gaps' then the completeness and frame properties of the system differ from those of the classical
exponential systems. This phenomenon is closely connected with the existence of
certain uniqueness sets for lacunary polynomials.Comment: 16 pages, 1 figur
Monotonicity theorem for subharmonic functions on manifolds
We provide a sharp monotonicity theorem about the distribution of subharmonic
functions on manifolds, which can be regarded as a new, measure theoretic form
of the uncertainty principle. As an illustration of the scope of this result,
we deduce contractivity estimates for analytic functions on the Riemann sphere,
the complex plane and the Poincar\'e disc, with a complete description of the
extremal functions, hence providing a unified and illuminating perspective of a
number of results and conjectures on this subject, in particular on the Wehrl
entropy conjecture by Lieb and Solovej. In this connection, we completely prove
that conjecture for SU(2), by showing that the corresponding extremals are only
the coherent states. Also, we show that the above (global) estimates admit a
local counterpart and in all cases we characterize also the extremal subsets,
among those of fixed assigned measure
Nucleus-nucleus interactions in very-high-energy cosmic ray experiments
A review of unusual results of experiments in cosmic rays which cannot be explained in the frame of the existing models of hadron interactions is presented. Requirements to features of a new model which are necessary for explanation of all observed unusual events and phenomena are formulated. A model of hadron interactions with production of QGM blobs with large orbital momentum is considered. Its possibilities for explanation of various unusual events and phenomena are discussed
Fourier Interpolation and Time-Frequency Localization
We prove that under very mild conditions for any interpolation formula f(x)=∑λ∈Λf(λ)aλ(x)+∑μ∈Mf^(μ)bμ(x) we have a lower bound for the counting functions nΛ(R1)+nM(R2)≥4R1R2−Clog2(4R1R2) which very closely matches recent interpolation formulas of Radchenko and Viazovska and of Bondarenko, Radchenko and Seip
Exponential lower bound for the eigenvalues of the time-frequency localization operator before the plunge region
We prove that the eigenvalues of the time-frequency
localization operator satisfy for , where and is arbitrary, improving on the result of Bonami, Jaming and Karoui, who
proved it for . The proof is based on the properties of
the Bargmann transform.Comment: 13 page