677,716 research outputs found
-right equivalence of analytic functions
Let be analytic functions.
We will show that if and then and
are -right equivalent, where denote ideal generated by and .Comment: 9 pages. Main result has been significantly improve
On Polyharmonic Interpolation
In the present paper we will introduce a new approach to multivariate
interpolation by employing polyharmonic functions as interpolants, i.e. by
solutions of higher order elliptic equations. We assume that the data arise
from or analytic functions in the ball We prove two main
results on the interpolation of or analytic functions in the
ball by polyharmonic functions of a given order of polyharmonicity
$p.
Motivic-type Invariants of Blow-analytic Equivalence
To a given analytic function germ , we
associate zeta functions , , defined
analogously to the motivic zeta functions of Denef and Loeser. We show that our
zeta functions are rational and that they are invariants of the blow-analytic
equivalence in the sense of Kuo. Then we use them together with the Fukui
invariant to classify the blow-analytic equivalence classes of Brieskorn
polynomials of two variables. Except special series of singularities our method
classifies as well the blow-analytic equivalence classes of Brieskorn
polynomials of three variables.Comment: 36 pages, 3 figure
Loop Integrals, R Functions and their Analytic Continuation
To entirely determine the resulting functions of one-loop integrals it is
necessary to find the correct analytic continuation to all relevant kinematical
regions. We argue that this continuation procedure may be performed in a
general and mathematical accurate way by using the function notation
of these integrals. The two- and three-point cases are discussed explicitly in
this manner.Comment: 10 pages (Latex), MZ-TH/93-1
Jointly maximal products in weighted growth spaces
It is shown that for any non-decreasing, continuous and unbounded doubling
function \om on , there exist two analytic infinite products and
such that the asymptotic relation |f_0(z)| + |f_1(z)| \asymp \om(|z|)
is satisfied for all in the unit disc. It is also shown that both functions
for satisfy , as , and
hence give examples of analytic functions for which the Nevanlinna
characteristic admits the regular slow growth induced by
Analytic cell decomposition and analytic motivic integration
The main results of this paper are a Cell Decomposition Theorem for Henselian
valued fields with analytic structure in an analytic Denef-Pas language, and
its application to analytic motivic integrals and analytic integrals over
\FF_q((t)) of big enough characteristic. To accomplish this, we introduce a
general framework for Henselian valued fields with analytic structure, and
we investigate the structure of analytic functions in one variable, defined on
annuli over . We also prove that, after parameterization, definable analytic
functions are given by terms. The results in this paper pave the way for a
theory of \emph{analytic} motivic integration and \emph{analytic} motivic
constructible functions in the line of R. Cluckers and F. Loeser
[\emph{Fonctions constructible et int\'egration motivic I}, Comptes rendus de
l'Acad\'emie des Sciences, {\bf 339} (2004) 411 - 416]
On generating functions of Hausdorff moment sequences
The class of generating functions for completely monotone sequences (moments
of finite positive measures on ) has an elegant characterization as the
class of Pick functions analytic and positive on . We establish
this and another such characterization and develop a variety of consequences.
In particular, we characterize generating functions for moments of convex and
concave probability distribution functions on . Also we provide a simple
analytic proof that for any real and with , the Fuss-Catalan or
Raney numbers , are the moments
of a probability distribution on some interval {if and only if}
and . The same statement holds for the binomial
coefficients , .Comment: 23 pages, LaTeX; Minor corrections and explanations added, literature
update. To appear in Transactions Amer. Math. So
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