110,240 research outputs found
Kissing numbers and transference theorems from generalized tail bounds
We generalize Banaszczyk's seminal tail bound for the Gaussian mass of a
lattice to a wide class of test functions. From this we obtain quite general
transference bounds, as well as bounds on the number of lattice points
contained in certain bodies. As applications, we bound the lattice kissing
number in norms by for , and also give
a proof of a new transference bound in the norm.Comment: Previous title: "Generalizations of Banaszczyk's transference
theorems and tail bound
Periodic correlation structures in bacterial and archaeal complete genomes
The periodic transference of nucleotide strings in bacterial and archaeal
complete genomes is investigated by using the metric representation and the
recurrence plot method. The generated periodic correlation structures exhibit
four kinds of fundamental transferring characteristics: a single increasing
period, several increasing periods, an increasing quasi-period and almost
noincreasing period. The mechanism of the periodic transference is further
analyzed by determining all long periodic nucleotide strings in the bacterial
and archaeal complete genomes and is explained as follows: both the repetition
of basic periodic nucleotide strings and the transference of non-periodic
nucleotide strings would form the periodic correlation structures with
approximately the same increasing periods.Comment: 23 pages, 6 figures, 2 table
Transference in spaces of measures
The transference theory for Lp spaces of Calderon, Coifman, and Weiss is a
powerful tool with many applications to singular integrals, ergodic theory, and
spectral theory of operators. Transference methods afford a unified approach to
many problems in diverse areas, which before were proved by a variety of
methods. The purpose of this paper is to bring about a similar approach to the
study of measures. Specifically, deep results in classical harmonic analysis
and ergodic theory, due to Bochner, de Leeuw-Glicksberg, Forelli, and others,
are all extensions of the classical F.&M. Riesz Theorem. We will show that all
these extensions are obtainable via our new transference principle for spaces
of measures.Comment: Also available at http://www.math.missouri.edu/~stephen/preprints
Transference Principles for Semigroups and a Theorem of Peller
A general approach to transference principles for discrete and continuous
operator (semi)groups is described. This allows to recover the classical
transference results of Calder\'on, Coifman and Weiss and of Berkson, Gillespie
and Muhly and the more recent one of the author. The method is applied to
derive a new transference principle for (discrete and continuous) operator
semigroups that need not be groups. As an application, functional calculus
estimates for bounded operators with at most polynomially growing powers are
derived, culminating in a new proof of classical results by Peller from 1982.
The method allows a generalization of his results away from Hilbert spaces to
\Ell{p}-spaces and --- involving the concept of -boundedness --- to
general Banach spaces. Analogous results for strongly-continuous one-parameter
(semi)groups are presented as well. Finally, an application is given to
singular integrals for one-parameter semigroups
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