Description of unconditional bases formed by values of the Dunkl kernels

On One Class of Non-Dissipative Operators

“…Expression (73) coincides per se with the well-known Dunkl kernel studied in [4], particularly for ν = 0, E(x, λ) = e iλx .…”

“…where c = b/b 1 4 ; f 1 + (x) and f 2 + (x) are the solutions of the Cauchy problems (19) and (24), respectively, besides,…”

“…(The function d α (λ) = 2 α Γ(α + 1)λ −α (J α (λ) + iJ α+1 (λ)) is said to be a Dunkl kernel, where J α (λ) is a Bessel function.) In contrast to [4], here the power dependence of the weight function is not supposed. The paper is dedicated to the study of one class of Volterra non-dissipative operators and to the construction of model representations for them.…”

“…Gubreyev and V.N. Levchuk [4] by which the study of Dunkl kernels is based on the analysis of a non-selfadjoint operator with two-dimensional imaginary component. (The function d α (λ) = 2 α Γ(α + 1)λ −α (J α (λ) + iJ α+1 (λ)) is said to be a Dunkl kernel, where J α (λ) is a Bessel function.)…”

“…The paper is dedicated to the study of one class of Volterra non-dissipative operators and to the construction of model representations for them. It turns out that many statements from [4] are general and can be obtained for "arbitrary" weight functions ϕ(x). In Section 1, general properties of the operator B are studied ant its characteristic function is calculated.…”