1,720,995 research outputs found
Perturbations of Bernstein-Durrmeyer operators on the simplex and best approximation properties
No full textWe study some modifications of Bernstein-Durrmeyer operators on a d-dimensional simplex in order to satisfy a best approximation property and an integro-differential Voronovskaja-type formula. Some applications concerning the representation of the solution of suitable evolution problems are also considered
Erratum to: Rate of convergence in Trotter's approximation theorem
No full textWe discuss in more details the validity of a previous theorem and we give some clarifications in order to justify the validity of some previous results concerning the application of some general theorems to Bernstein operators
Approximation processes for resolvent operators
No full textWe introduce some general sequences of linear operators obtained from classical approximation processes which turn to be useful in the approximation of the resolvent operators of the generator of suitable C_0-semigroups. The main aim is the possibility of representing the resolvent operators in terms of classical approximation operators
Steklov operators in spaces of continuous functions in two variables
No full textIn this paper we introduce a sequence of Steklov-type operators in spaces of continuous real functions in two variables. The integral mean is performed over a rotated rectangle and this allows us to obtain a more general Voronovskaja-type formula for these operators. We study convergence and Voronovskaja-type formulas both with respect to a weighted uniform norm and with respect to the uniform norm in suitable spaces
Kernel estimates for a Schrodinger type operator
No full textIn this paper the principal result obtained is the estimate for the heat kernel associated to a Schr"odinger type operator. This estimate improves a similar estimate obtained in our previous paper with respect to the dependence on spatial component
Quantitative approximation of semigroups and resolvent operators by iterates of Stancu operators
No full textIn this paper we consider some quantitative estimates on the
convergence of suitable combinations of iterates of Stancu
operators to the resolvent operator of a C_0-semigroup in the
context of spaces of continuous functions on the d-dimensional
simplex
Steklov operators and their associated semigroups
No full textWe consider Steklov operators in spaces of continuous functions on the real line and on a bounded interval. We study the connections of these operators with some second-order degenerate parabolic problems establishing a general Voronovskaja type formula
Trotter’s approximation of semigroups and order of convergence in C2,α-spaces
No full textAbstractWe improve the quantitative estimate of the convergence in Trotter’s approximation theorem and obtain a representation of the resolvent operators in terms of iterates of linear operators on its whole domain. In the context of the standard simplex we give some estimates for functions of class C2,α which considerably improve some previous estimates and allow one to establish a partial inverse result
Kernel estimates for elliptic operators with unbounded diffusion, drift and potential terms
No full textIn this paper we prove that the heat kernel associated to the operator
satisfies
[k(t,x,y) leq c_1e^{lambda_0 t+ c_2t^{-gamma}}left(frac{1+|y|^alpha}{1+|x|^alpha}
right)^{frac{b}{2alpha}}
frac{(|x||y|)^{-frac{N-1}{2}-rac{1}{4}(eta-alpha)}}{1+|y|^alpha}
e^{-frac{sqrt{2}}{eta-alpha+2}left(|x|^{frac{eta-alpha+2}{2}}+ |y|^{frac{eta-alpha+2}{2}}
right)}
]
for t>0,,|x|, |y|ge 1, where in , are positive constants, is the largest eigenvalue of the operator , and , in the case where N>2, alpha>2 and eta>alpha -2. The proof is based on the relationship between the log-Sobolev inequality and the ultracontractivity of a suitable semigroup in a weighted space
Approximation of cosine functions and Rogosinski type operators
No full textWe study some quantitative estimates of the convergence of the iterates of some Rogosinski type operators to their associated cosine functions. We also consider a general cosine counterpart of the quantitative version of Trotter’s theorem on the approximation of C0-semigroups
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