9 papers · 1 filter
A note on n-divisible positive definite functions
Saulius Norvidas
Let be the family of continuous positive definite functions on . For an integer , a is called -divisible if there is $g\i…
On large sieve inequalities involving pth powers of trigonometric polynomials
Saulius Norvidas
In this paper, we extend the large sieve type estimates to sums involving pth powers of trigonometric polynomials. An approach to such estimates that does not rely on the usual L^2…
On the deterministic property for characteristic functions of several variables
Saulius Norvidas
Assume that is the characteristic function of a probability measure on . Let . We study the following extrapolation problem: under what conditions on the neighb…
A note on uniqueness of extension for characteristic functions
Saulius Norvidas
Let be the characteristic function of a probability measure. We study the following question: Is it true that for any closed interval on , which does not contain…
A note on analytic continuation of characteristic functions
Saulius Norvidas
We derive necessary and sufficient conditions for a continuous bounded function to be a characteristic function of a probability measure. The Cauchy transform of…
A note on harmonic continuation of characteristic function
Saulius Norvidas
We propose a necessary and sufficient condition for a real-valued function on the real line to be a characteristic function of a probability measures. The statement is given in ter…