Abstract
In this chapter we specify further the results of Chaps. 4, 5 and 6 for semi-separable operators. The chapter consists of three sections (and two subsections). The first section deals with completeness results for a class of discrete semi-separable operators studied in Section V.3 of [29]. Such operators are quite different from the Leslie operators considered in Chap. 8. The theory developed in Chap. 4 is useful in studying completeness for these discrete semi-separable operators. The second section deals with completeness results for semi-separable integral operators. The results in Chapter IX of [32], together with the results developed in Chaps. 5 and 6, are used to derive completeness results for the semi-separable integral operators. The final section has a preparatory character, not directly related to semi-separable operators. We collect some results about the fundamental solution of an ordinary differential equation, and we present an explicit resolvent formula for a class of integral operators and related Volterra operators which will play a role in the next chapter and in Chap. 11.
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Kaashoek, M.A., Verduyn Lunel, S.M. (2022). Semi-Separable Operators and Completeness. In: Completeness Theorems and Characteristic Matrix Functions. Operator Theory: Advances and Applications, vol 288. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-04508-0_9
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DOI: https://doi.org/10.1007/978-3-031-04508-0_9
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