6,736 research outputs found
Topological convolution algebras
In this paper we introduce a new family of topological convolution algebras
of the form , where is a Borel
semi-group in a locally compact group , which carries an inequality of the
type for where pre-assigned,
and is a constant. We give a sufficient condition on the measures
for such an inequality to hold. We study the functional calculus and
the spectrum of the elements of these algebras, and present two examples, one
in the setting of non commutative stochastic distributions, and the other
related to Dirichlet series.Comment: Corrected version, to appear in Journal of Functional Analysi
On free stochastic processes and their derivatives
We study a family of free stochastic processes whose covariance kernels
may be derived as a transform of a tempered measure . These processes
arise, for example, in consideration non-commutative analysis involving free
probability. Hence our use of semi-circle distributions, as opposed to
Gaussians. In this setting we find an orthonormal bases in the corresponding
non-commutative of sample-space. We define a stochastic integral for our
family of free processes
The Fock space in the slice hyperholomorphic setting
In this paper we introduce and study some basic properties of the Fock space
(also known as Segal-Bargmann space) in the slice hyperholomorphic setting. We
discuss both the case of slice regular functions over quaternions and also the
case of slice monogenic functions with values in a Clifford algebra. In the
specific setting of quaternions, we also introduce the full Fock space. This
paper can be seen as the beginning of the study of infinite dimensional
analysis in the quaternionic setting.Comment: to appear in "Hypercomplex Analysis: New Perspectives and
Applications", Trends in Mathematics, Birkhauser, Basel, S. Bernstein et al.
ed
Estimating Lattice Artifacts from Flowed SU(2) Calorons
Lattice computations of the high-temperature topological susceptibility of
QCD receive lattice-spacing corrections and suffer from systematics arising
from the type and depth of gradient flow. We study the lattice spacing
corrections to semi-analytically by exploring the behavior
of discretized Harrington-Shepard calorons under the action of different forms
of gradient flow. From our study we conclude that is definitely
too small of a time extent to study the theory at temperatures of order
and we explore how the amount of gradient flow influences the
continuum extrapolation.Comment: 10 pages, 8 figures (published version
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