The regular part of second-order differential sectorial forms with lower-order terms

Abstract

Abstract. We present a formula for the regular part of a sectorial form that represents a general linear second-order differential expression that may include lower-order terms. The formula is given in terms of the original coefficients. It shows that the regular part is again a differential sectorial form and allows to characterise when also the singular part is sectorial. While this generalises earlier results on pure second-order differential expressions, it also shows that lower-order terms truly introduce new behaviour.

Arlinskii's Iteration and its Applications

“…An analogous decomposition of not necessarily non-negative sesquilinear forms can be found in the recent paper of Di Bella and Trapani [8, § 4]. We remark that the idea of decomposing (densely defined) sesquilinear forms into regular and singular parts goes back to Simon [21], and there are recent results in the same spirit in the theory of partial differential equations (see for example [4,25,26]).…”

“…We remark that the idea of decomposing (densely defined) sesquilinear forms into regular and singular parts goes back to Simon [22], and there are recent results in the same spirit in the theory of partial differential equations (see for example [4,9,26]).…”

Operators on anti-dual pairs: Lebesgue decomposition of positive operators

“…In the last 50 years quite a number of authors have made significant contributions to the vast literature of non-commutative Lebesgue-Radon-Nikodym theory -here we mention only Ando [2], Gudder [17], Inoue [22], Kosaki [23] and Simon [30], and from the recent past Di Bella and Trapani [7], Corso [8][9][10], ter Elst and Sauter [13], Gheondea [16], Hassi et al [18][19][20][21], Sebestyén and Titkos [32], Szűcs [34], Vogt [46].…”