Laplace contour integrals and linear differential equations

Norbert Steinmetz (Technische Universität Dortmund)

29-Sep-2020, 13:00-14:00 (3 years ago)

Abstract: Any linear differential equation with coefficients of degree one $$w^{(n)}+\sum_{j=0}^{n-1}(a_j+b_jz)w^{(j)}=0$$ has solutions that may be represented as Laplace contour integrals $$f(z)=\frac1{2\pi i}\int_C\phi(t)e^{-zt}\,dt.$$ We will discuss the main properties of these solutions and determine their order of growth, asymptotics, Phragm\'en-Lindel\"of indicator, distribution of zeros, Nevanlinna functions $T(r,f)$ and $N(r,1/f)$, and the existence of sub-normal and polynomial solutions.

complex variablesdynamical systems

Audience: researchers in the topic


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