2003/12/04 by Jaap Korevaar, Korevaar, Jaap
Computer Science · Engineering · Mathematics · #11N05 #42A38 #44A10 #46F20 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary: 40E05 #Secondary: 11M45 #Stability and Controllability of Differential Equations #math.CA #math.CV #msc:11M45 #msc:11N05 #msc:40E05 #msc:42A38 #msc:44A10 #msc:46F20
paper · pdf · doi:10.48550/arxiv.math/0312104
11 pages, 1 figure
arxiv created 2003/12/04 · openalex publication_date 2003/12/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The prime number theorem provided the chief impulse for complex Tauberian theory, in which the boundary behavior of a transform in the complex plane plays a crucial role. We consider Laplace transforms of bounded functions. Our Tauberian theorem does not allow first-order poles on the imaginary axis, but any milder singularities, characterized by pseudofunction boundary behavior, are permissible. In this context we obtain a useful Tauberian theorem by exploiting Newman's `contour method'.