Anzeige
Erschienen in:
2010 | OriginalPaper | Buchkapitel
Elementary Functional Analysis
verfasst von : Weijiu Liu
Erschienen in: Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Elementary functional analysis, such as Hilbert spaces, Sobolev spaces, and linear operators, is collected in this chapter for the reader’s convenience. Since elementary stabilization results are presented without using functional analysis, readers may skip this chapter and come back when needed. In this book, ℕ denotes the set of all nonnegative natural numbers, ℂ denotes the set of complex numbers, ℝ
n
denotes the
n
-dimensional Euclidean space, and ℝ = ℝ
1
denotes the real line. Points in ℝ
n
will be denoted by
x
= (
x
1
, …,
x
n
), and its norm is defined by
$$\|\mathbf{x}\| = \left(\sum_{i = 1}^{n}x_{i}^{2}\right)^{\frac{1}{2}}.$$