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- Wolfgang Arendt, Werner Kratz, Alan McIntosh, Dieter Beschorner

In the first part inequalities for solutions of Riccati matrix difference equations are obtained which correspond to the linear Hamiltonian difference system ⌬ X s A X q B U , ⌬U s C X y A T U , k k k q 1 k k k k kq1 k k where A , B , C , X , U are n = n-matrices with symmetric B and C. If the k k k k k k k matrices X are invertible, then the matrices Q s U… (More)

- Ondrej Dosly, Werner Kratz
- 2008

We consider symplectic difference systems involving a spectral parameter together with general separated boundary conditions. We establish the so-called oscillation theorem which relates the number of finite eigenvalues less than or equal to a given number to the number of focal points of a certain conjoined basis of the symplectic system. Then we prove… (More)

In this paper we prove the differentiability properties of solutions of nonlinear dynamic equations on time scales with respect to parameters. This complements the previous work of the first and third authors regarding the existence and continuity of solutions with respect to parameters. In addition, we treat separately time scale dynamic equations which… (More)

- Werner Kratz, Roman Simon Hilscher, Roman Šimon Hilscher
- 2010

In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the… (More)

- Martin Bohner, Werner Kratz, Roman Simon Hilscher, Roman Šimon Hilscher
- 2011

In this paper, we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. Our results generalize the known theory of linear Hamiltonian systems in two respects. Namely, we allow nonlinear dependence of the coefficients on the spectral parameter and at the same… (More)

- Werner Kratz, Markus Tentler, Werne Kratz
- 2007

In this article we treat the algebraic eigenvalue problem for real, symmetric, and banded matrices of size N × N , say. For symmetric, tridi-agonal matrices, there is a well-known two-term recursion to evaluate the characteristic polynomials of its principal submatrices. This recursion is of complexity O(N) and it requires additions and multiplications… (More)

- Iva Drimalová, Werner Kratz
- 2016

In this paper we study a general even order symmetric Sturm–Liouville matrix differential equation, whose leading coefficient may be singular on the whole interval under consideration. Such an equation is new in the current literature, as it is equivalent with a system of Sturm–Liouville equations with different orders. We identify the so-called normal form… (More)

- Werner Kratz
- 2009

We consider eigenvalue problems for self-adjoint Sturm-Liouville difference equations of any even order. It is well-known that such problems with Dirichlet boundary conditions can be transformed into an algebraic eigenvalue problem for a banded, real-symmetric matrix, and vice versa. In this article it is shown that such a transform exists for general… (More)

- Werner Kratz
- 1998

In this paper we give a survey on the theory of quadratic func-tionals. Particularly the relationships between positive definiteness and the asymptotic behaviour of Riccati matrix differential equations, and between the oscillation properties of linear Hamiltonian systems and Rayleigh's principle are demonstrated. Moreover, the main tools form control… (More)