1,721,001 research outputs found
Integral-type operators on continuous function spaces on the real line,
No full textIn this paper we introduce and study a sequence of integral-type positive
linear operators acting on a sufficiently large continuous function space
which contains wide classes of weighted spaces of continuous functions on the
real line. These operators depend on three given functions \alpha
,\beta, and \gamma\in C(R),
\gamma bounded, and generalize the classical Gauss-Weierstrass
convolution operators
The main motivation to introduce these operators rests on the aim to construct
a sequence of positive linear operators which satisfies an asymptotic formula
(with respect to a given weighted norm) whose limit operator is a second order
elliptic differential operator of the form%
Lu=\alpha u’’+\beta u’+\gamma u.
The operators which we introduce in this paper satisfy, indeed, such an
asymptotic formula opening the way to a possible investigation to find
suitable domains on which the differential operator L generates a C0 -semigroup of positive operators which can be represented in terms of
iterates of these operators. However this aspect will be developed in a
forthcoming paper.
Besides the connection with semigroup theory, our operators seems to have a
possible interest in the weighted approximation of continuous functions on the
real line for a wide class of weights.
We start our analysis by first introducing a sequence of integral-type
positive linear operators depending only on the functions \alpha and \beta
. We discuss their approximation properties in several spaces of continuous
functions and we give some estimates of the rate of convergence. We also
establish an asymptotic formula together with a saturation result.
Subsequently we study some shape preserving properties. Finally, in the last
section, by modifying these operators, we obtain a further approximation
process which involves the function \gamma and which verifies analogous
qualitative properties, including the general above mentioned asymptotic formula
On a class of positive C_0-semigroups on weighted continuous function spaces,
No full textThis paper is mainly concerned with the study of the generators of those positive
C0-semigroups on weighted continuous function spaces that leave invariant a given closed sublattice
of bounded continuous functions and whose relevant restrictions are Feller semigroups.
Additive and multiplicative perturbation results for this class of generators are also established.
Finally, some applications concerning multiplicative perturbations of the Laplacian on
Rn, n ≥ 1, and degenerate second-order differential operators on unbounded real intervals are
showed
Multiplicative perturbations of the Laplacian and related approximation problems, to appear in Journal of Evolution Equations
No full textOf concern are multiplicative perturbations of the Laplacian acting
on weighted spaces of continuous functions on R^N. It is proved that such differential operators, defined on
their maximal domains, are pre-generators of positive
quasicontractive C_0-semigroups of operators that fulfil the
Feller property. Accordingly, these semigroups are associated with a
suitable probability transition function and hence with a Markov
process on R^N. An approximation
formula for these semigroups is also stated in terms of iterates of
integral operators that generalize the classical Gauss-Weierstrass
operators. Some applications of such approximation formula are
finally shown concerning both the semigroups and the associated
Markov processes
Le vie del grano nella Puglia centrale. Il sistema delle tre piazze del piano delle fosse di Cerignola
No full text
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