312 research outputs found
On powers of Stieltjes moment sequences, II
We consider the set of Stieltjes moment sequences, for which every positive
power is again a Stieltjes moment sequence, we and prove an integral
representation of the logarithm of the moment sequence in analogy to the
L\'evy-Khinchin representation. We use the result to construct product
convolution semigroups with moments of all orders and to calculate their Mellin
transforms. As an application we construct a positive generating function for
the orthonormal Hermite polynomials.Comment: preprint, 21 page
Quiz Games as a model for Information Hiding
We present a general computation model inspired in the notion of information
hiding in software engineering. This model has the form of a game which we call
quiz game. It allows in a uniform way to prove exponential lower bounds for
several complexity problems of elimination theory.Comment: 46 pages, to appear in Journal of Complexit
The Jacobi matrices approach to Nevanlinna-Pick problems
A modification of the well-known step-by-step process for solving
Nevanlinna-Pick problems in the class of \bR_0-functions gives rise to a
linear pencil , where and are Hermitian tridiagonal
matrices. First, we show that is a positive operator. Then it is proved
that the corresponding Nevanlinna-Pick problem has a unique solution iff the
densely defined symmetric operator is self-adjoint and some
criteria for this operator to be self-adjoint are presented. Finally, by means
of the operator technique, we obtain that multipoint diagonal Pad\'e
approximants to a unique solution of the Nevanlinna-Pick problem
converge to locally uniformly in \dC\setminus\dR. The proposed
scheme extends the classical Jacobi matrix approach to moment problems and
Pad\'e approximation for \bR_0-functions.Comment: 24 pages; Section 5 is modifed; some typos are correcte
Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions
This paper is aimed to show the essential role played by the theory of
quasi-analytic functions in the study of the determinacy of the moment problem
on finite and infinite-dimensional spaces. In particular, the quasi-analytic
criterion of self-adjointness of operators and their commutativity are crucial
to establish whether or not a measure is uniquely determined by its moments.
Our main goal is to point out that this is a common feature of the determinacy
question in both the finite and the infinite-dimensional moment problem, by
reviewing some of the most known determinacy results from this perspective. We
also collect some properties of independent interest concerning the
characterization of quasi-analytic classes associated to log-convex sequences.Comment: 28 pages, Stochastic and Infinite Dimensional Analysis, Chapter 9,
Trends in Mathematics, Birkh\"auser Basel, 201
Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
The holomorphic anomaly equations describe B-model closed topological strings
in Calabi-Yau geometries. Having been used to construct perturbative
expansions, it was recently shown that they can also be extended past
perturbation theory by making use of resurgent transseries. These yield formal
nonperturbative solutions, showing integrability of the holomorphic anomaly
equations at the nonperturbative level. This paper takes such constructions one
step further by working out in great detail the specific example of topological
strings in the mirror of the local CP2 toric Calabi-Yau background, and by
addressing the associated (resurgent) large-order analysis of both perturbative
and multi-instanton sectors. In particular, analyzing the asymptotic growth of
the perturbative free energies, one finds contributions from three different
instanton actions related by Z_3 symmetry, alongside another action related to
the Kahler parameter. Resurgent transseries methods then compute, from the
extended holomorphic anomaly equations, higher instanton sectors and it is
shown that these precisely control the asymptotic behavior of the perturbative
free energies, as dictated by resurgence. The asymptotic large-order growth of
the one-instanton sector unveils the presence of resonance, i.e., each
instanton action is necessarily joined by its symmetric contribution. The
structure of different resurgence relations is extensively checked at the
numerical level, both in the holomorphic limit and in the general
nonholomorphic case, always showing excellent agreement with transseries data
computed out of the nonperturbative holomorphic anomaly equations. The
resurgence relations further imply that the string free energy displays an
intricate multi-branched Borel structure, and that resonance must be properly
taken into account in order to describe the full transseries solution.Comment: 63 pages, 54 images in 24 figures, jheppub-nosort.sty; v2: corrected
figure, minor changes, final version for CM
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