FUNCTIONS ON THE REAL LINE WITH NONNEGATIVE FOURIER-TRANSFORMS

Citation
T. Kawazoe et al., FUNCTIONS ON THE REAL LINE WITH NONNEGATIVE FOURIER-TRANSFORMS, Tohoku Mathematical Journal, 46(3), 1994, pp. 311-320
Citations number
8
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
ISSN journal
0040-8735
Volume
46
Issue
3
Year of publication
1994
Pages
311 - 320
Database
ISI
SICI code
0040-8735(1994)46:3<311:FOTRLW>2.0.ZU;2-W
Abstract
Unlike an integrable function on the unit circle which has the nonnega tive Fourier coefficients and is square-integrable near the origin, an integrable function on the real line which has the nonnegative Fourie r transform and is square-integrable near the origin is not always squ are-integrable on the real line. We give some examples, and consider a n additional condition which guarantees the global square-integrabilit y. Moreover, we treat an analogous problem for an integrable function on the real line which has non-negative wavelet coefficients of the Fo urier transform and is square-integrable near the origin.