Classification of Distributions by the Arithmetic Means of Their Fourier Series

Author: Kádár, F.

Source: Acta Mathematica Hungarica, Volume 89, Number 3, November 2000 , pp. 221-232(12)

Publisher: Springer

Buy & download fulltext article:


Price: $47.00 plus tax (Refund Policy)


We consider the class C^m of functions that are m times differentiable on the one-dimensional torus group G = R/2Z with respect to addition mod 2; and the class of D^m of distributions of order at most m. Clearly, D^m can be identified as the dual space of C^m. One of our main results says that a formal trigonometric series $$\sum {c_ne^{inx}}$$ is the Fourier series of a distribution in D^m if and only if the sequence of its arithmetic means _N (u) as distributions is bounded for all u ∈ C; or equivalently, if sup ‖_N¦_D < ∞. Another result says that the arithmetic mean _N F of a distribution converges to F in the strong topology of D^m if F ∈ D^m−1, which is not true in general if F ∈ D^m.

Document Type: Regular Paper

Affiliations: Vág Utca 5 1133 Budapest Hungary E-mail: FERI@MARECO.HU

Publication date: November 1, 2000

Related content


Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content

Text size:

A | A | A | A
Share this item with others: These icons link to social bookmarking sites where readers can share and discover new web pages. print icon Print this page