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F Comput. , pages 57–69. Springer, Berlin, 1987. Vol. 64 (2009) The Suboptimal Nehari Problem 59 [20] Martin Weiss and George Weiss. Optimal control of stable weakly regular linear systems. Math. Control Signals Systems, 10(4):287–330, 1997. [21] 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) [7] 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) [8] 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) [9] 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.