Boundary Value Problems, Weyl Functions, and Differential Operators

Abstract

The foundations of this outstanding book series were laid in 1944. Until the end of the 1970s, a total of 77 volumes appeared, including works of such distinguished mathematicians as Carathéodory, Nevanlinna and Shafarevich, to name a few. The series came to its name and present appearance in the 1980s. In keeping its well-established tradition, only monographs of excellent quality are published in this collection. Comprehensive, in-depth treatments of areas of current interest are presented to a readership ranging from graduate students to professional mathematicians. Concrete examples and applications both within and beyond the immediate domain of mathematics illustrate the import and consequences of the theory under discussion.

Self-Adjoint Dirac Operators on Domains in $$\mathbb {R}^3$$

“…and is formally the same as in the case of ordinary boundary triples, see [14,35]. Note that (2.1) implies, in particular, that Γ 0 ker(T − λ) is injective for λ ∈ ρ(A 0 ).…”

“…if Ω is bounded, this is essentially a consequence of unique continuation (for details see [14,Section 8.3]) and if Ω is unbounded this fact can be found in…”

“…The concept of quasi boundary triples is a generalization of ordinary and generalized boundary triples; cf. [14,27,35,36]. We note that the operator T in the above definition is not unique if the dimension of G is infinite.…”

Self-Adjoint Extensions with Friedrichs Lower Bound

“…Standard extension schemes produce convenient classifications of the whole family of extensions. It can be shown within the modern theory of boundary triplets [2], or equivalently the classical 'universal' parametrization by Grubb [7], and in fact the very original extension theory by Kreȋn [9], Višik [12], and Birman [3], that the extensions of S can be labelled as follows.…”

Range-kernel characterizations of operators which are adjoint of each other

“…where the second equality tells us that the adjoint of a densely defined linear relation is always a (single valued) operator. For further information on linear relation we refer the reader to [1,2,4,10].…”