Anzeige
Erschienen in:
2010 | OriginalPaper | Buchkapitel
Fourier Analysis on ℝ n
verfasst von : Michael Ruzhansky, Ville Turunen
Erschienen in: Pseudo-Differential Operators and Symmetries
Verlag: Birkhäuser Basel
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
In this chapter we review basic elements of Fourier analysis on ℝ
n
. Consequently, we introduce spaces of distributions, putting emphasis on the space of tempered distributions
S′
(ℝ
n
). Finally, we discuss Sobolev spaces and approximation of functions and distributions by smooth functions. Throughout, we fix the measure on ℝ
n
to be Lebesgue measure. For convenience, we may repeat a few definitions in the context of ℝ
n
although they may have already appeared in Chapter C on measure theory. From this point of view, the present chapter can be read essentially independently. The notation used in this chapter and also in Chapter 2 is 〈ξ〉 = (1 + |ξ|
2
)
1/2
where |ξ| = (ξ
1
2
+ ξ
n
2
)
1/2
, ξ ∈ ℝ
n
.