A note on positive definite distributions

Norvidas, Saulius

doi:10.1016/j.indag.2013.01.008

Use this url to cite publication: https://cris.mruni.eu/cris/handle/007/34779

A note on positive definite distributions

Details

Type of publication

Straipsnis Web of Science ir Scopus duomenų bazėje / Article in Web of Science and Scopus database (S1)

Author(s)

Author	Affiliation
Norvidas, Saulius	Komunikacijos institutas / Institute of Communication	Vilniaus universitetas

Title

A note on positive definite distributions

[en]

Publisher (trusted)

Elsevier

Date Issued

Date
2013

Extent

p. 505-517

Is part of

Indagationes mathematicae. Amsterdam : Elsevier BV, 2013, vol. 24, no. 3.

Research Area

Gamtos mokslai / Natural Sciences (N)

Field of Science

Matematika / Mathematics (N001)

Keywords (lt)

Keywords (en)

Abstract (en)

We provide necessary and sufficient conditions for a tempered distribution F∈S′(R)F∈S′(R) to be positive definite. A generalized Cauchy transform View the MathML sourceF˜ of FF is used as a numerical continuation of FF to the open upper and lower half-planes in CC. In fact, our necessary and sufficient conditions for FF are determined completely by the properties of the restriction of View the MathML sourceF˜ to the imaginary axis in CC. The main result is given in terms of completely monotonic and absolutely monotonic functions.