1. Cautionary example 2. Criterion for essential self-adjointness 3. Examples of essentially self-adjoint operators 4. Appendix: Friedrichs' canonical self-adjoint extensions 5. The following has been well understood for 70-120 years, or longer, naturally not in contemporary terminology. The differential operator T = d 2 dx 2 on L 2 [a, b] or L 2 (R) is a prototypical natural unbounded operator...

In this paper, we study Dirichlet operators on certain smooth Banach spaces. We establish the well-known Kato's inequality in our general infinite dimensional setting. By applying this,we show the essential self-adjointness of Dirichlet operators with non-constant diffusion part on certain smooth Banach spaces. We also provide an approximation criterion for essential self-adjointness of Dirichl...

We derive Povzner–Wienholtz-type self-adjointness results form× m matrix-valued Sturm–Liouville operators T = R [

Introduction 2 1. Self-adjointness of Schrödinger operators 3 1.0. Solving the Schrödinger equation 3 1.1. Linear operators in Hilbert space 7 1.2. Criteria for (essential) self-adjointness 13 1.3. Application to Schrödinger operators 18 2. Hardy-Rellich inequalities 21 2.0. Relative boundedness 21 2.1. Weighted estimates 24 2.2. Explicit bounds 26 3. Spectral properties of radially periodic Sc...

We specify the structure of completely positive operators and quantum Markov semigroup generators that are symmetric with respect to a family inner products, also providing new information on order extreme points in some previously studied cases.

and Applied Analysis 3 Table 1: Nonlinear self-adjointness of (3). f g V Selfadjointness ∀(f u ̸ = 0) ∀ C 1 + C 2 eαt Nonlinear ∀(f u ̸ = 0) C 5 (C 1 + C 2 eαt)(C 3 + C 4 x) Nonlinear ∀(f u ̸ = 0) C 5 ∫f(u)du C 1 + C 2 eαt +(C 3 + C 4 e αt )e x/C5 Nonlinear C 0 ( ̸ = 0) C 1 + C 2 u C 1 e (C2/C0)x+αtu + b(t, x) Weak α is a nonzero constant; b(t, x) satisfies (27). Equation (23) can be satisfied by t...