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O.Y. Kushel 《Linear algebra and its applications》2011,435(11):2722-2730
A generalization of the definition of an oscillatory matrix based on the theory of cones is given in this paper. The positivity and simplicity of all the eigenvalues of a generalized oscillatory matrix are proved. Classes of generalized even and odd oscillatory matrices are introduced. Spectral properties of the obtained matrices are studied. Criteria of generalized even and odd oscillation are given. Examples of generalized even and odd oscillatory matrices are presented. 相似文献
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Journal of Dynamics and Differential Equations - We generalize the concepts of D-stability and additive D-stability of matrices. For this, we consider a family of unbounded regions defined in terms... 相似文献
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Pseudo-Hermitian operators are studied within the theory of singular perturbations. Necessary and sufficient conditions for
the spectra of such operators to be real are presented. A criterion for the similarity of a pseudo-Hermitian operator to an
Hermitian one is established. 相似文献
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We establish the eigenvalue interlacing property (i.e. the smallest real eigenvalue of a matrix is less than the smallest real eigenvalue of any of its principal submatrices) for the class of matrices introduced by Kotelyansky (all principal and almost principal minors of these matrices are positive). We show that certain generalizations of Kotelyansky and totally positive matrices possess this property. We also prove some interlacing inequalities for the other eigenvalues of Kotelyansky matrices. 相似文献
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Olga Kushel 《The Ramanujan Journal》2013,32(1):109-124
In this paper, we study the continued fraction y(s,r) which satisfies the equation y(s,r)y(s+2r,r)=(s+1)(s+2r?1) for $r > \frac{1}{2}$ . This continued fraction is a generalization of the Brouncker’s continued fraction b(s). We extend the formulas for the first and the second logarithmic derivatives of b(s) to the case of y(s,r). The asymptotic series for y(s,r) at ∞ are also studied. The generalizations of some Ramanujan’s formulas are presented. 相似文献
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