self-adjointness
Look at other dictionaries:
Self-adjoint operator — In mathematics, on a finite dimensional inner product space, a self adjoint operator is one that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose.… … Wikipedia
Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… … Wikipedia
Extensions of symmetric operators — In functional analysis, one is interested in extensions of symmetric operators acting on a Hilbert space. Of particular importance is the existence, and sometimes explicit constructions, of self adjoint extensions. This problem arises, for… … Wikipedia
Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… … Wikipedia
Dirac delta function — Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention… … Wikipedia
Gårding domain — In mathematics, a Gårding domain is a concept in the representation theory of topological groups. The concept is named after the mathematician Lars Gårding.Let G be a topological group and let U be a strongly continuous unitary representation of… … Wikipedia
Spectral theory of ordinary differential equations — In mathematics, the spectral theory of ordinary differential equations is concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation. In his dissertation Hermann Weyl… … Wikipedia
Friedrichs extension — In functional analysis, the Friedrichs extension is a canonical self adjoint extension of a non negative densely defined symmetric operator. It is named after the mathematician Kurt Friedrichs. This extension is particularly useful in situations… … Wikipedia
State (functional analysis) — In functional analysis, a state on a C* algebra is a positive linear functional of norm 1. The set of states of a C* algebra A , sometimes denoted by S ( A ), is always a convex set. The extremal points of S ( A ) are called pure states. If A has … Wikipedia
Hamburger moment problem — In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence { αn : n = 1, 2, 3, ... }, does there exist a positive Borel measure μ on the real line such that:alpha n = int {… … Wikipedia
