Bounds for characteristic values of entire matrix pencils
For an infinite set of \(n\) by \(n\) matrices \(\{A_k\}\) with \(A_0=I_n\), the author studies the entire matrix pencil \(f(z) = \sum_{k=0}^\infty \;\frac{z^k}{(k!)^{^\gamma}}\;A_k\) for complex \(z\) and \(\gamma > 0\). The characteristic values of \(f\) are defined as the zeros of \(\det(f(z))\). If there are infinitely many characteristic values for \(f\) and the given set of matrices, the author gives an upper bound for the sum of reciprocals (in absolute value) of the characteristic values and upper and lower bounds for the smallest characteristic value of \(f\).
scientific article; zbMATH DE number 2116539