التفاصيل البيبلوغرافية
| العنوان: |
Convolution equation and operators on the Euclidean motion group. |
| المؤلفون: |
Bassey, U. N.1, Edeke, U. E.2 ueedeke@gmail.com |
| المصدر: |
Journal of Nigerian Society of Physical Sciences. Nov2024, Vol. 6 Issue 4, p1-8. 8p. |
| مصطلحات موضوعية: |
*MATHEMATICAL convolutions, *DIRAC function, *ALGEBRA, *DIFFERENTIAL operators, *EUCLIDEAN geometry |
| مستخلص: |
Let G = R²xSO(2) be the Euclidean motion group, let g be the Lie algebra of G and letU(g) be the universal enveloping algebra of g. ThenU(g) is an infinite dimensional, linear associative and non-commutative algebra consisting of invariant differential operators on G. The Dirac measure on G is represented by δG, while the convolution product of functions or measures on G is represented by *. Among other notable results, it is demonstrated that for each u in U(g), there is a distribution E on G such that the convolution equation u * E = δG is solved by method of convolution. Further more, it is established that the (convolution) operator A' : C∞c (G) → C∞(G), which is defined as A' f = f * Tnδ(t) extends to a bounded linear operator on L²(G), for f ∈ C∞c (G), the space of infinitely differentiable functions on G with compact support. Furthermore, we demonstrate that the left convolution operator LT denoted as LT f = T * f commutes with left translation, for T ∈ D'(G). [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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