Was (wer) ist operator sections - definition

LINEAR OPERATOR DEFINED ON A DENSE LINEAR SUBSPACE

Closed operator; Closeable operator; Closable operator; Closed unbounded operator; Closure of an operator; Unbounded linear operator

Transfer operator

PUSHFORWARD ON THE SPACE OF MEASURABLE FUNCTIONS

Ruelle operator; Perron-Frobenius operator; Perron-Frobenius Operator; Frobenius-Perron operator; Bernoulli operator; Ruelle-Frobenius-Perron operator; Frobenius–Perron operator; Perron–Frobenius operator

In mathematics, the transfer operator encodes information about an iterated map and is frequently used to study the behavior of dynamical systems, statistical mechanics, quantum chaos and fractals. In all usual cases, the largest eigenvalue is 1, and the corresponding eigenvector is the invariant measure of the system.

https://en.wikipedia.org/wiki/Transfer_operator

Del

VECTOR'S DIFFERENTIAL OPERATOR

Nabla constant; Atled; Nabla operator; Del operator; Vector differential; Vector differential operator; Gradient operator; Divergence operator

Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a one-dimensional domain, it denotes the standard derivative of the function as defined in calculus.

https://en.wikipedia.org/wiki/Del

Del

VECTOR'S DIFFERENTIAL OPERATOR

Nabla constant; Atled; Nabla operator; Del operator; Vector differential; Vector differential operator; Gradient operator; Divergence operator

·noun Share; portion; part.

Wikipedia

Unbounded operator

In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases.

The term "unbounded operator" can be misleading, since

"unbounded" should sometimes be understood as "not necessarily bounded";
"operator" should be understood as "linear operator" (as in the case of "bounded operator");
the domain of the operator is a linear subspace, not necessarily the whole space;
this linear subspace is not necessarily closed; often (but not always) it is assumed to be dense;
in the special case of a bounded operator, still, the domain is usually assumed to be the whole space.

In contrast to bounded operators, unbounded operators on a given space do not form an algebra, nor even a linear space, because each one is defined on its own domain.

The term "operator" often means "bounded linear operator", but in the context of this article it means "unbounded operator", with the reservations made above. The given space is assumed to be a Hilbert space. Some generalizations to Banach spaces and more general topological vector spaces are possible.

https://en.wikipedia.org/wiki/Unbounded operator