Quasi-projection operators with applications to differential-difference expansions

D. Costarelli, A. Krivoshein, M. Skopina, G. Vinti

Research output

Abstract

A large class of multivariate quasi-projection operators is studied. These operators are sampling-type expansions ∑k∈Zd ck(f)ψ(Aj·−k), where A is a matrix and the coefficients ck(f) are associated with a tempered distribution ψ˜. 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.

Original languageEnglish
Article number124623
JournalApplied Mathematics and Computation
Volume363
DOIs
Publication statusPublished - 15 Dec 2019

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Projection Operator
Mathematical operators
Strings
Tempered Distribution
Differential-difference Equations
Approximation Order
Compatibility Conditions
Lp-norm
Difference equations
Engineering Application
Compatibility
Error Estimates
Smoothness
Sampling
Coefficient
Operator
Class

Scopus subject areas

  • Computational Mathematics

Cite this

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title = "Quasi-projection operators with applications to differential-difference expansions",
abstract = "A large class of multivariate quasi-projection operators is studied. These operators are sampling-type expansions ∑k∈Zd ck(f)ψ(Aj·−k), where A is a matrix and the coefficients ck(f) are associated with a tempered distribution ψ˜. 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.",
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AU - Costarelli, D.

AU - Krivoshein, A.

AU - Skopina, M.

AU - Vinti, G.

PY - 2019/12/15

Y1 - 2019/12/15

N2 - A large class of multivariate quasi-projection operators is studied. These operators are sampling-type expansions ∑k∈Zd ck(f)ψ(Aj·−k), where A is a matrix and the coefficients ck(f) are associated with a tempered distribution ψ˜. 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.

AB - A large class of multivariate quasi-projection operators is studied. These operators are sampling-type expansions ∑k∈Zd ck(f)ψ(Aj·−k), where A is a matrix and the coefficients ck(f) are associated with a tempered distribution ψ˜. 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.

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KW - Strang-Fix conditions

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