S. Norvidas

activity

20192022

collaborators

13 papers

math.CA2022

A note on n-divisible positive definite functions

Saulius Norvidas

Let $P D (R)$ be the family of continuous positive definite functions on $R$ . For an integer $n > 1$ , a $f \in P D (R)$ is called $n$ -divisible if there is $g\i…

math.CA2022

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…

math.FA2020

On exposed functions in Bernstein spaces of functions of exponential type

Saulius Norvidas

For $σ > 0$ , the Bernstein space \ $B_{σ}^{1}$ consists of those $L^{1} (R)$ \ functions whose Fourier transforms are supported by $[- σ, σ]$ . Since $B_{σ}^{1}$ is separable and dual to some Banac…

math.CA2020

On the deterministic property for characteristic functions of several variables

Saulius Norvidas

Assume that $f$ is the characteristic function of a probability measure $μ_{f}$ on $R^{n}$ . Let $σ > 0$ . We study the following extrapolation problem: under what conditions on the neighb…

math.CA2020

A note on uniqueness of extension for characteristic functions

Saulius Norvidas

Let $f : R \to C$ be the characteristic function of a probability measure. We study the following question: Is it true that for any closed interval $I$ on $R$ , which does not contain…

math.CA2020

A note on analytic continuation of characteristic functions

Saulius Norvidas

We derive necessary and sufficient conditions for a continuous bounded function $f : R \to C$ to be a characteristic function of a probability measure. The Cauchy transform $K_{f}$ of…

math.CA2020

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…

math.FA2020

On functional calculus for Hermitian elements of Banach algebras: the norm and spectral radius

Saulius Norvidas

Let $A$ be a complex unital Banach algebra. An element $a \in A$ is said to be Hermitian, if $∥ exp (i t a) ∥ = 1$ for all $t \in R$ . In the case of the algebra of bounded linear…

math.CA2020

On the imaginary part of the characteristic function

Saulius Norvidas

Suppose that $f$ is the characteristic function of a probability measure on the real line $R$ . In this paper, we deal with the following problem posed by N.G. Ushakov: Is it true…

math.CA2020

Approximation of entire functions of exponential type by trigonometric sums

Saulius Norvidas

Let $σ > 0$ . For $1 \leq p \leq \infty$ , the Bernstein space $B_{σ}^{p}$ is a Banach space of all $f \in L^{p} (R)$ such that $f$ is bandlimited to $σ$ ; that is, the distributional Fourier trans…

math.FA2020

On positive definite distributions

Saulius Norvidas

We provide necessary and sufficient conditions for a tempered distribution $F \in S^{'} (R)$ to be positive definite. A generalized Cauchy transform $F$ of $F$ is used as a…

math.PR2020

A note on powers of the characteristic function

Saulius Norvidas

Let $C H (R)$ denote the family of characteristic functions of probability measures (distributions) on the real line $R$ . We study the following question: given an integer $n > 1$ , do…

math.CA2019

On a sampling expansion with partial derivatives for functions of several variables

Saulius Norvidas

Let $B_{σ}^{p}$ , $1 \leq p < \infty$ , $σ > 0$ , denote the space of all $f \in L^{p} (R)$ such that the Fourier transform of $f$ (in the sense of distributions) vanishes outside $[- σ, σ]$ …