Unbounded operator – Knowledge and References

Explore chapters and articles related to this topic

Second and Higher Order Linear Differential Equations

Published in Vladimir A. Dobrushkin, Applied Differential Equations, 2022

Differentiation gives us an example of a linear unbounded operator. Let D denote differentiation with respect to the independent variable (x in our case), that is, Dy=y′=dydx so D=ddx.

On the Cauchy problem for a periodic rotation-two-component μ-Hunter–Saxton system

View Article

Journal Information

Published in Applicable Analysis, 2019

Yunxi Guo, Shaoyong Lai

Let X and Y be two Hilbert spaces such that Y is continuously and densely embedded in X. Let be a topological isomorphism, and let and be the norms of the Banach spaces X and Y, respectively. Let L(Y, X) denote the space of all bounded linear operators from Y to X. In particular, it is denoted by L(X) if . If A is an unbounded operator, we denote the domain of A by D(A). [A, B] denotes the commutator of two linear operators A and B. The linear operator A belongs to , where is a real number, if generates a -semigroup such that . The inner product in is denoted by , particularly the inner product is .