English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A population process with constant birth rates λn ≡ λ and death rates μn ≡ μ is supplied with strong linear killing rates γn = γn for n ∈ N0. The process is analyzed in view of its spectral representation: The underlying orthogonal polynomials are seen to be Lommel polynomials Rn,ν(x), considered as functions in their parameter ν. Regarding the Stieltjes transform of their orthogonality measure, we recognize that it is purely discrete and given by the zeros of a Bessel function Jν−1(x) in its order. Qualitative and quantitative results for the zeros are worked out via methods from the theory of Bessel functions and from regular perturbation theory. The same ideas are applied successfully to study the spectrum for associated Meixner polynomials, corresponding to linear birth and death rates.

Spectral Analysis of Birth-and-Death Processes with and without Killing via Perturbation