Convolution Type Operators on ℝN
In this chapter, we are going to introduce a Banach algebra Bp of operators onLp(ℝ N ) which become band-dominated operators acting onlP(ℤ N ,X) withX= Lp([0, 1)N) after a suitable discretization and which are, thus, subject to the general theory developed in the previous chapter. Prominent members of this class are the Fourier convolution operators, certain pseudodifferential operators as well as operators in finite differences. We employ the close relationship between operators in Bpand their discretizations to study the local invertibility at infinity (which is related with the Fredholmness) as well as the applicability of the finite section method for operators in Bp.
KeywordsLimit Operator Essential Spectrum Fredholm Operator Angular Point Operator Spectrum
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