13,520 research outputs found
On the R-boundedness of stochastic convolution operators
The -boundedness of certain families of vector-valued stochastic
convolution operators with scalar-valued square integrable kernels is the key
ingredient in the recent proof of stochastic maximal -regularity,
, for certain classes of sectorial operators acting on spaces
, . This paper presents a systematic study of
-boundedness of such families. Our main result generalises the
afore-mentioned -boundedness result to a larger class of Banach lattices
and relates it to the -boundedness of an associated class of
deterministic convolution operators. We also establish an intimate relationship
between the -boundedness of these operators and the boundedness of
the -valued maximal function. This analysis leads, quite surprisingly, to an
example showing that -boundedness of stochastic convolution operators fails
in certain UMD Banach lattices with type .Comment: to appear in Positivit
Convolution equations on lattices: periodic solutions with values in a prime characteristic field
These notes are inspired by the theory of cellular automata. A linear
cellular automaton on a lattice of finite rank or on a toric grid is a discrete
dinamical system generated by a convolution operator with kernel concentrated
in the nearest neighborhood of the origin. In the present paper we deal with
general convolution operators. We propose an approach via harmonic analysis
which works over a field of positive characteristic. It occurs that a standard
spectral problem for a convolution operator is equivalent to counting points on
an associate algebraic hypersurface in a torus according to the torsion orders
of their coordinates.Comment: 30 pages, a new editio
Quantum statistical mechanics over function fields
In this paper we construct a noncommutative space of ``pointed Drinfeld
modules'' that generalizes to the case of function fields the noncommutative
spaces of commensurability classes of Q-lattices. It extends the usual moduli
spaces of Drinfeld modules to possibly degenerate level structures. In the
second part of the paper we develop some notions of quantum statistical
mechanics in positive characteristic and we show that, in the case of Drinfeld
modules of rank one, there is a natural time evolution on the associated
noncommutative space, which is closely related to the positive characteristic
L-functions introduced by Goss. The points of the usual moduli space of
Drinfeld modules define KMS functionals for this time evolution. We also show
that the scaling action on the dual system is induced by a Frobenius action, up
to a Wick rotation to imaginary time.Comment: 28 pages, LaTeX; v2: last section expande
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