Kernel Identities and Vectorial Regularization

Abstract

We present the method of "vectorial regularization" to prove kernel identities. This method is applied to derive both known kernel identities, e.g. ${\dot{\mathcal{B}}}_{xy}={\dot{\mathcal{B}}}_x{\hat{\otimes }}_{\epsilon }{\dot{\mathcal{B}}}_y$, ${\mathcal{D}}_{L^1,xy}^{\prime }={\mathcal{D}}_{L^1,x}^{\prime }{\hat{\otimes }}_{\pi }{\mathcal{D}}_{L^1,y}^{\prime }$, as well as new ones: ${\dot{\mathcal{B}}}_{xy}^{\prime }={\dot{\mathcal{B}}}_x^{\prime }{\hat{\otimes }}_{\epsilon }{\dot{\mathcal{B}}}_y^{\prime }$ and ${\mathcal{D}}_{L^1,xy}={\mathcal{D}}_{L^1,x}{\hat{\otimes }}_{\pi }{\mathcal{D}}_{L^1,y}$.

References in corpus (1)

• Convolvability and regularization of distributions