2016/08/12 by R. Lakshmi Lavanya, Lavanya, R. Lakshmi
Mathematics · #Mathematical Analysis and Transform Methods #advanced mathematical theories #Advanced Harmonic Analysis Research
paper · pdf · doi:10.48550/arxiv.1608.03713
We study the general form of isomorphisms on the algebra of compactly supported complex-valued continuous functions defined on a locally compact Hausdorff space (the proof of which works for the algebra of Ck-differentiable functions on a Ck-manifold as well). We obtain using only topological techniques, that any such map is a composition of a homeomorphism of the locally compact space (resp. Ck-diffeomorphism), and an automorphism of the field of complex numbers. In the particular case when X is a locally compact group, and the map preserves convolution products, the resulting homeomorphism is also a group isomorphism. An application of this gives a characterisation of the Fourier transform on the algebra of Schwartz-Bruhat functions on locally compact Abelian groups.