Characteristic matrices and spectral properties of evolutionary systems

In this paper we introduce the notion of a characteristic matrix for a large class of unbounded operators and study the precise connection between characteristic matrices and spectral properties of evolutionary systems. In particular, we study so-called multiplicity theorems. Several examples will illustrate our results

[1]  Toshiki Naito,et al.  Functional Differential Equations With Infinite Delay , 1991 .

[2]  Odo Diekmann,et al.  A new short proof of an old folk theorem in functional-differential equations , 1991 .

[3]  Linearization of boundary eigenvalue problems , 1991 .

[4]  M. A. Kaashoek,et al.  Classes of Linear Operators Vol. I , 1990 .

[5]  I. Gohberg,et al.  Classes of Linear Operators , 1990 .

[6]  Generalized Jordan chains and two bifurcation theorems of Krasnoselskii , 1989 .

[7]  Sjoerd Verduyn Lunel.  Exponential type calculus for linear delay equations , 1989 .

[8]  A multiplicity theorem for hyperbolic systems , 1988 .

[9]  Odo Diekmann,et al.  Perturbation theory for dual semigroups , 1987 .

[10]  Aloisio Neves,et al.  On the spectrum of evolution operators generated by hyperbolic systems , 1986 .

[11]  Angus E. Taylor,et al.  Introduction to functional analysis, 2nd ed. , 1986 .

[12]  Root functions of boundary eigenvalue operator functions , 1986 .

[13]  M. A. Kaashoek.  Analytic equivalence of the boundary eigenvalue operator function and its characteristic matrix function , 1986 .

[14]  Odo Diekmann,et al.  Perturbation theory for dual semigroups. I. The sun-reflexive case , 1986 .

[15]  Wilhelm Schappacher,et al.  Spectral Properties of Finite-Dimensional Perturbed Linear Semigroups , 1985 .

[16]  G. Webb.  Theory of Nonlinear Age-Dependent Population Dynamics , 1985 .

[17]  John A. Burns,et al.  Linear Functional Differential Equations as Semigroups on Product Spaces , 1983 .

[18]  M. C. Delfour,et al.  The Largest Class of Hereditary Systems Defining a C 0 Semigroup on the Product Space , 1980, Canadian Journal of Mathematics.

[19]  M. A. Kaashoek,et al.  Minimal Factorization of Matrix and Operator Functions , 1980 .

[20]  M. A. Kaashoek,et al.  Equivalence, linearization, and decomposition of holomorphic operator functions , 1978 .

[21]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[22]  F. Kappel,et al.  An elementary divisor theory for autonomous linear functional differential equations , 1976 .

[23]  内藤 敏機,et al.  On autonomous linear functional differential equations with infinite retardations = 無限の遅れを持つ自励線形函数微分方程式について , 1976 .

[24]  Jack K. Hale,et al.  Functional differential equations with infinite delays , 1974 .

[25]  Daniel B. Henry,et al.  Linear autonomous neutral functional differential equations , 1974 .

[26]  I. Gohberg,et al.  AN OPERATOR GENERALIZATION OF THE LOGARITHMIC RESIDUE THEOREM AND THE THEOREM OF ROUCHÉ , 1971 .

[27]  B. Levinger,et al.  A folk theorem in functional differential equations , 1968 .

[28]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[29]  J. Schwartz,et al.  Linear Operators. Part I: General Theory. , 1960 .

[30]  N. Jacobson.  Lectures In Abstract Algebra , 1951 .

[31]  E. Hille.  Functional Analysis And Semi-Groups , 1948 .

[32]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .