S. Norvidas

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20192022

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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.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.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…