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Eigenvalue conditions for convergence of singularly perturbed matrix exponential functions. (English) Zbl 1227.15010
This paper deals with the convergence of sequences of matrix exponential functions $$t\rightarrow e^{tA^{-1}_{k}}$$, for $$t>0$$, with $$A_k\rightarrow A$$, $$A_k$$ being nonsingular and $$A$$ being nilpotent. The convergence of the sequences is investigating in the pointwise and almost uniform senses, with the results obtained in terms of the eigenvalues of $$A^{-1}_{k}$$. Furthermore, considering the exponential as a Schwartz distribution, necessary and sufficient conditions for weak* convergence are presented.

##### MSC:
 15A16 Matrix exponential and similar functions of matrices 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 15A18 Eigenvalues, singular values, and eigenvectors 46F10 Operations with distributions and generalized functions
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