Which amalgams are convolution algebras? Academic Article uri icon

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abstract

  • We determine necessary and sufficient conditions on a locally compact abelian group G G for the amalgam ( L p , l q ) ( G ) \left ( {{L^p},{l^q}} \right )\left ( G \right ) to be an algebra under convolution. If q > 1 , G q > 1,G must be compact; if p > 1 , G p > 1,G must be discrete. If p 1 p \geqslant 1 and q 1 q \leqslant 1 , the amalgam is always an algebra.

publication date

  • January 1, 1985