## Rocky Mountain Journal of Mathematics

### Extremal Problems of Interpolation Theory

#### Article information

Source
Rocky Mountain J. Math. Volume 35, Number 3 (2005), 819-841.

Dates
First available in Project Euclid: 5 June 2007

https://projecteuclid.org/euclid.rmjm/1181069708

Digital Object Identifier
doi:10.1216/rmjm/1181069708

Mathematical Reviews number (MathSciNet)
MR2150310

Zentralblatt MATH identifier
1094.47026

#### Citation

Helton, J. William; Sakhnovich, L.A. Extremal Problems of Interpolation Theory. Rocky Mountain J. Math. 35 (2005), no. 3, 819--841. doi:10.1216/rmjm/1181069708. https://projecteuclid.org/euclid.rmjm/1181069708

#### References

• N.I. Akhiezer, On a minimum problem in function theory and the number of roots of an algebraic equation inside the unit disc, in Topics in Interpolation Theory, Oper. Theory Adv. Appl., vol. 95, Birkhaüser, Basel, 1997, pp. 19-35.
• J.A. Ball, I. Gohberg and L. Rodman, Interpolation of rational matrix functions, Birkhaüser, Basel, 1990.
• H. Dym, J Contractive matrix functions, reproducing kernel Hilber spaces and interpolation, CBMS, No. 71, Amer. Math. Soc., Providence, 1989.
• J.A. Engwerda, A.C.M. Ran and A.L. Rijvabeer, Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation, Linear Algebra Appl. 186 (1993), 255-275.
• A. Ferrante and B.C. Levy, Hermitian solutions of the equation $X=Q + NX^-1 N^*$, Linear Algebra Appl. 247 (1996), 359-373. (See the reduction process in the proof of Theorem 2.8.)
• M. Green and D.J.N. Limebeer, Linear robust control, Prentice-Hall, Englewood Cliffs, NJ, 1995.
• J.W. Helton, J. Ball, C. Johnson and C. Palmer, Operator theory, analytic functions, matrices and electrical engineering, CBMS Regional Conf. Ser. in Math., vol. 68, Amer. Math. Soc., Providence, 1987.
• T.S. Ivanchenko and L.A. Sakhnovich, Operator identities in the theory of interpolation problems, Soviet J. Contemporary Math. Anal. 22 (1987), 84-94.
• H. Kimura, State space approach to the classical interpolation problem and its applications, Lecture Notes in Control Inform. Sci., vol. 135, Springer, New York, 1989, pp. 243-275.
• --------, Chain scattering approach to $H^\infty$-control, Birkhaüser, Boston, 1997.
• V.V. Peller and N.J. Young, Superoptimal analytic approximations of matrix functions, J. Funct. Anal. 120 (1994), 300-343.
• A.C.M.Ran and M.C.B. Reurings, On the nonlinear matrix equation $X+A^\starF(X)A+Q$ solution and perturbation theory, Linear Algebra Appl. 346 (2002), 15-26.
• L. Sakhnovich, Interpolation theory and its applications, Kluwer Acad. Publ., Dordrecht, 1997.
• N.J. Young, The Nevalinna-Pick problem for matrix-valued functions, J. Operator Theory 15 (1986), 289-265.
• K. Zhou, J. Doyle and K. Glover, Robust and optimal control, Prentice-Hall, Upper Saddle River, NJ, 1996.