Matrix Convolution Operators

Part of the Lecture Notes in Mathematics book series (LNM, volume 1956)

In this Chapter, we study the basic structures of matrix convolution operators Tσ : f ∈ L p (G, M n ) ↦f * σ∈ L p (G,M n ). Noncommutativity of the matrix multiplication necessitates the introduction of the left convolution operator Lσ : f ↦σ *ℓ f for a consistent duality theory. We first characterise these operators and show they are translation invariant operators satisfying some continuity condition.We also determine when these operators are weakly compact on L1 and L spaces.


Abelian Group Harmonic Function Compact Group Convolution Operator Left Translation 
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© Springer-Verlag Berlin Heidelberg 2008

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