Let μn be a sequence of discrete measures on the unit circle T = ℝ/ℤ with μn (0) = 0, and μn ((-δ,δ)) → 1, as n → ∞. We prove that the sequence of convolution operators (f ⁕ μn)(x) is strong sweeping ...

Consider a discrete group G and a bounded self-adjoint convolution operator T on l2 (G); let σ (T) be the spectrum of T. The spectral theorem gives a unitary isomorphism U between l2 (G) and a direct ...

In this unit the characteristics and inter-relations of linear (continuous and discrete) signals and systems will be discussed. Principles of sampling theory, aliasing, correlation, convolution, and ...

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