On the number of zeros of analytic functions in a neighborhood of a Fuchsian singular point with real spectrum
The authors consider the differential equation \(L(f)=0\), where \(L= a_0(t) \partial^n+ a_1(t)\partial^{n-1}+\dots +a_{n- 1}(t)\partial+a_n(t)\), assuming that \(f\) is analytic in some subset \(K\) of the complex plane, and \(U\) is an open domain that contains \(K\), and finally all the coefficients \(a_j(t)\) \((j=0,1,2,3,\dots, n-1)\), are analytic and bounded in \(U\). The authors find an upper bound for the number of isolated zeros of \(f(t)\) in \(K\) in terms of the magnitudes of the coefficients \(a_j(t)\) in \(U\).
number of zeros of analytic functions in a neighborhood of a fuchsian singular point with real spectrum
upper bound for the number of isolated zeros
scientific article; zbMATH DE number 942618