Singular perturbation theorems for semibounded operators

The Trotter Product Formula for Perturbations of Semibounded Operators

Perturbation and Interpolation Theorems for the H∞-Calculus with Applications to Differential Operators

Abstract. We prove comparison theorems for the H∞-calculus that allow to transfer the property of having a bounded H∞-calculus from one sectorial operator to another. The basic technical ingredient are suitable square function estimates. These comparison results provide a new approach to perturbation theorems for the H∞-calculus in a variety of situations suitable for applications. Our square f...

Erratum to: Perturbation and interpolation theorems for the H∞-calculus with applications to differential operators

In our article [2], some of the general boundedness results in Sects. 7 and 8 for the H∞-functional calculusmay not be correct as stated sincewhen applying [4, 1.2.4] our proofs use implicitly certain inclusions of interpolation spaces, which were not stated as assumptions and which do not hold in all generality. We would like to point out here that, with these assumptions added we obtain corre...

Existence and Perturbation Theorems for Nonlinear Maximal Monotone Operators in Banach Spaces by Felix E. Browder

Such a set G is said to be maximal monotone if it is maximal among monotone sets in the sense of set inclusion, and a mapping T is said to be maximal monotone if its graph G(T) is a maximal monotone set. For reflexive Banach spaces X and mappings T with D(T)~X, the basic result obtained independently by Browder [2] and Minty [20] states that if T is a monotone operator from D(T)=X to X* which i...

Singular perturbation theory

When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...