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F Comput. , pages 57–69. Springer, Berlin, 1987. Vol. 64 (2009) The Suboptimal Nehari Problem 59  Martin Weiss and George Weiss. Optimal control of stable weakly regular linear systems. Math. Control Signals Systems, 10(4):287–330, 1997.  Hans Zwart. Transfer functions for infinite-dimensional systems. , 52(3-4):247–255, 2004. Ruth F. O. nl Mark R. uk Submitted: July 17, 2008. Revised: November 9, 2008. Integr. equ. oper. 1007/s00020-009-1680-3 Integral Equations and Operator Theory Eigenvalues of Integral Operators Defined by Smooth Positive Definite Kernels J.
15. MR 0453964 (56 #12216)  A. Fern´ andez, F. Mayoral, F. Naranjo, C. A. S´ anchez-P´erez, Spaces of p-integrable functions with respect to a vector measure, Positivity 10 (2006), no. 1, 1–16. MR 2223581 (2006m:46053)  A. Fern´ andez, F. Mayoral, F. Naranjo, C. A. S´ anchez-P´erez, Spaces of integrable functions with respect to a vector measure and factorizations through Lp and Hilbert spaces, J. Math. Anal. Appl. 330 (2007), no. 2, 1249–1263. MR 2308439 (2008f:46034)  J. Lindenstrauss and L.
9 and is proven similarly. 4. The inverse of the (1, 1) component of V on the open unit disc is the transfer function of the output stable and input-output stable system AX −2 ∗ TX B XA −1 −BTX −1 TX . (41) Proof. 1 together with the identity −2 ∗ A − BTX B XA = AX , which is easily proven using only the definition of TX . 4. Since the characteristic functions of the two systems are inverses it follows that the product of the two transfer functions equals the identity for z in a neighborhood of zero.