On stable operator polynomials

被引：0

作者：

Rozhankivs'ka M.I. ^{[1
]}

机构：

来源：

Journal of Mathematical Sciences | 1998年 / 90卷 / 5期

关键词：

Hilbert Space; Continue Fraction; Test Fraction; Positive Component; Equivalent Fraction;

D O I：

10.1007/BF02433982

中图分类号：

学科分类号：

摘要：

We attempt to generalize the classical theorem of Wall on the stability of an ordinary numerical polynomial to the operator-valued case. It is shown that such a generalization is admissible if the coefficients of the operator polynomial are uniformly positive commuting operators in Hilbert space. ©1998 Plenum Publishing Corporation.

引用

页码：2446 / 2449

页数：3

共 6 条

[1]

Jones, W., Thron, W., (1980) Continued Fractions, , Addison-Wesley, Reading, MA

[2]

Kazimirs'kii, P.S., (1981) Decomposition of Matrix Polynomials into Factors, , [in Ukrainian], Naukova Dumka, Kiev

[3]

Marmershtein, I.I., On a property of the spectrum of a family of linear operators and its applications to the study of solutions of difference and operator equations (1979) Teor. Funkts. Funkts. Anal. Pril., 32

[4]

Syavavko, M.S., (1988) Fractional-Analytic Approximation of Solutions of Linear Problems, , Preprint No. 12-88, Institute for Applied Problems of Mathematics and Mechanics of the Academy of Sciences of the Ukrainian SSR, L'vov

[5]

Hurwitz, A., Über die bedingungen, unter welchen eine gleichung nur würzel mit negativen reelen teilen besitzt (1891) Math. Ann., 39, pp. 279-284

[6]

Wall, H.S., (1948) Analytic Theory of Continued Fractions, , Van Nostrand, New York

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