Tag Archives: approximation to the identity

DMat0101, Notes 3: The Fourier transform on L^1

1. Definition and main properties. For , the Fourier transform of is the function Here denotes the inner product of and : Observe that this inner product in is compatible with the Euclidean norm since . It is easy to … Continue reading

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DMat0101, Notes 2: Convolution, Dense subspaces and interpolation of operators

1. Convolutions and approximations to the identity We restrict our attention to the Euclidean case . As we have seen the space is a vector space; linear combinations of functions in remain in the space. There is however a `product’ … Continue reading

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