Functions on the real line with nonnegative fourier transforms

Takeshi Kawazoe, Yoshikazu Onoe, Kazuya Tachizawa

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Unlike an integrable function on the unit circle which has the nonnegative Fourier coefficients and is square-integrable near the origin, an integrable function on the real line which has the nonnegative Fourier transform and is square-integrable near the origin is not always square-integrable on the real line. We give some examples, and consider an additional condition which guarantees the global square-integrability. Moreover, we treat an analogous problem for an integrable function on the real line which has non-negative wavelet coefficients of the Fourier transform and is squareintegrable near the origin.

Original languageEnglish
Pages (from-to)311-320
Number of pages10
JournalTohoku Mathematical Journal
Volume46
Issue number3
DOIs
Publication statusPublished - 1994

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Real Line
Fourier transform
Non-negative
Wavelet Coefficients
Fourier coefficients
Unit circle
Integrability

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Functions on the real line with nonnegative fourier transforms. / Kawazoe, Takeshi; Onoe, Yoshikazu; Tachizawa, Kazuya.

In: Tohoku Mathematical Journal, Vol. 46, No. 3, 1994, p. 311-320.

Research output: Contribution to journalArticle

Kawazoe, Takeshi ; Onoe, Yoshikazu ; Tachizawa, Kazuya. / Functions on the real line with nonnegative fourier transforms. In: Tohoku Mathematical Journal. 1994 ; Vol. 46, No. 3. pp. 311-320.
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