Authors: Steinmetz, Norbert
Title: Laplace contour integrals and linear differential equations
Language (ISO): en
Abstract: The purpose of this paper is to determine the main properties of Laplace contour integrals Λ(z)=12πi∫Cϕ(t)e−ztdt that solve linear differential equations L[w](z):=w(n)+∑j=0n−1(aj+bjz)w(j)=0. This concerns, in particular, the order of growth, asymptotic expansions, the Phragmén–Lindelöf indicator, the distribution of zeros, the existence of sub-normal and polynomial solutions, and the corresponding Nevanlinna functions.
Subject Headings: Linear differential equation
Laplace contour integral
Asymptotic expansion
Order of growth
Phragmén–Lindelöf indicator
Sub-normal solution
Function of complete regular growth
Distribution of zeros
Issue Date: 2021-07-17
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Appears in Collections:Fakultät für Mathematik

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