The Functional Analytic Part: Scales of Hilbert Spaces and Boundary Triples
In this chapter, we present the necessary quantitative analysis for a single operator in a Hilbert space. Basically, we introduce the natural scale of Hilbert spaces associated with a non-negative operator (Sect. 3.2) and to general closed operators (Sect. 3.3). We need quantitative norm estimates on the resolvent and other functions of such closed operator as well as norm bounds on related embeddings especially when dealing with families of operators in Chap. 4. The closed operators we are dealing here with, are more general than sectorial operators.
KeywordsHilbert Space Quadratic Form Elliptic Boundary Quantum Graph Couple Boundary
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