Reverse generalized Bessel matrix differential equation, polynomial solutions, and their properties

On the Polynomial Solutions of the Generalized Lame Differential Equation

According to Heine (see Marden [l, §9], or Marden [2]),1 there exist some choices F(z) of the polynomial R(z) corresponding to each of which equation (1.1) has a polynomial solution S(z). The 5(z) were called Stieltjes polynomials by Van Vleck in honor of the man who first studied the location of their zeros relative to those of P(z). For a similar reason, we shall call the F(z) Van Vleck polyn...

Differential Polynomial Rings of Triangular Matrix Rings

The Generalized Bessel Matrix Polynomials

Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...

Analytic properties of matrix Riccati equation solutions

For matrix Riccati equations of platoontype systems and of systems arising from PDEs, assuming the coefficients are analytic functions in a suitable domain, the analyticity of the stabilizing solution is proved under various hypotheses. In addition, general results on the analytic behavior of stabilizing solutions are developed. I. NONSTANDARD RICCATI EQUATIONS In [10], [7] and elsewhere contin...

Parametric solutions to the generalized discrete Sylvester matrix equation MXN - X = TY and their applications

In this paper, an explicit, analytical and complete solution to the generalized discrete Sylvester matrix equation M X N − X = T Y which is closely related with several types of matrix equations in control theory is obtained. The proposed solution has a neat and elegant form in terms of the Krylov matrix, a block Hankel matrix and an observability matrix. Based on the proposed solution, an expl...