6533b7dbfe1ef96bd1270119

RESEARCH PRODUCT

Multiplication of distributions in any dimension: Applications to δ-function and its derivatives

Fabio Bagarello

subject

Pure mathematicsApplied MathematicsMultiplication of distributionsDirac delta functionFunction (mathematics)symbols.namesakeDistribution functionDimension (vector space)symbolsDelta functionDelta functionsMultiplicationSettore MAT/07 - Fisica MatematicaMathematical PhysicsComputer Science::DatabasesAnalysisMathematics

description

In two previous papers the author introduced a multiplication of distributions in one dimension and he proved that two one-dimensional Dirac delta functions and their derivatives can be multiplied, at least under certain conditions. Here, mainly motivated by some engineering applications in the analysis of the structures, we propose a different definition of multiplication of distributions which can be easily extended to any spatial dimension. In particular we prove that with this new definition delta functions and their derivatives can still be multiplied.

yearjournalcountryeditionlanguage
2009-04-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2007.04.050