A large class of multivariate quasi-projection operators is studied. These operators are sampling-type expansions. Error estimates in Lp-norm, 2 ≤ p <∞, are obtained under the so-called weak compatibility conditions for ψ and ψ, and the Strang-Fix conditions for ψ. Approximation order depends on the smoothness of f and on the order of the compatibility and the Strang-Fix conditions. A number of examples aimed at engineering applications are provided. A special attention is payed to the quasi-projection operators associated with differential-difference expansions. Applications to solving some differential-difference equations are presented.
Quasi-projection operators with applications to differential-difference expansions
Costarelli D.Membro del Collaboration Group
;Vinti G.Membro del Collaboration Group
2019
Abstract
A large class of multivariate quasi-projection operators is studied. These operators are sampling-type expansions. Error estimates in Lp-norm, 2 ≤ p <∞, are obtained under the so-called weak compatibility conditions for ψ and ψ, and the Strang-Fix conditions for ψ. Approximation order depends on the smoothness of f and on the order of the compatibility and the Strang-Fix conditions. A number of examples aimed at engineering applications are provided. A special attention is payed to the quasi-projection operators associated with differential-difference expansions. Applications to solving some differential-difference equations are presented.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.