NonEuclidean functional analysis and electronics
Author:
J. William Helton
Journal:
Bull. Amer. Math. Soc. 7 (1982), 164
MSC (1980):
Primary 35D55, 30E05, 32M15, 46J15, 47A45, 47A65, 47A68, 47B35, 47B38, 47B50, 94C05; Secondary 22E50
DOI:
https://doi.org/10.1090/S027309791982150017
MathSciNet review:
656197
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References  Similar Articles  Additional Information

[A] D. Z. Arov, Darlington realization of matrixvalued functions, Izv. Akad. Nauk SSSR Ser Mat. 37 (1973), 12991331; English transl. in Math. USSR Izv. 7 (1973). MR 357820

[AAKl] V. M. Adamajan, D. Z. Arov and M. G. Krein, Analytic properties of Schmidt pairs for a Hankel operator and the generalized SchurTakagi problem, Math. USSRSb. 15 (1971), 3173.

[AAK2] V. M. Adamajan, D. Z. Arov and M. G. Krein, Infinite block Hankel matrices and their connection with the interpolation problem, Akad. Nauk Armenia SSR Isvestia Mat. 6 (1971); Amer. Math. Soc. Transl. (2) 111 (1978), 133156.
 Gr. Arsene, Zoia Ceauşescu, and C. Foiaş, On intertwining dilations. VIII, J. Operator Theory 4 (1980), no. 1, 55–91. MR 587368

[An] T. Ando, On a pair of commutative contractions, Acta Sci. Math. (Szeged) 24 (1963), 8890. MR 155193
 Joseph A. Ball, Interpolation problems of PickNevanlinna and Loewner types for meromorphic matrix functions, Integral Equations Operator Theory 6 (1983), no. 6, 804–840. MR 719106, https://doi.org/10.1007/BF01691925
 Joseph A. Ball and J. William Helton, Lie groups over the field of rational functions, signed spectral factorization, signed interpolation, and amplifier design, J. Operator Theory 8 (1982), no. 1, 19–64. MR 670177

[BH2] J. A. Ball and J. W. Helton, Interpolation with outer functions and gain equalization amplifiers, Proc. of the Internat. Conf. on Math. Theory of Circuits and Systems (Delft, July 1979).
 Joseph A. Ball and J. William Helton, Subinvariants for analytic mappings on matrix balls, Analysis 1 (1981), no. 3, 217–226. MR 660718, https://doi.org/10.1524/anly.1981.1.3.217

[BH4] J. A. Ball and J. W. Helton, A BeurlingLax theorem for the Lie group U (m, n) which contains most classical interpolation theory, J. Operator Theory (to appear).

[BH5] J. A. Ball and J. W. Helton, Factorization results related to shifts in an indefinite metric (manuscript).

[Bdr] J. Border, Nonlinear Hardy spaces and electrical power transfer, U.C.S.D. Thesis, 1979.

[C] W. Chen, Theory and design of broadband matching networks, Pergamon, Oxford, 1976.

[CK] Y. T. Chan and E. Kuh, A general matching theory and its applications to tunnel a diode amplifier, IEEE Trans. C.T. 13 (1966), 618.

[CL] L. Chua and PenMinLin, Computer aided analysis of electronic circuits: Algorithms and computational techniques, PrenticeHall, Englewood Cliffs, New Jersey, 1975.

[C] D. Clark, On the spectra of bounded hermitian Hankel matrices, Amer. J. Math. 90 (1968), 627656. MR 231112

[D] W. F. Donoghue, Monotone matrix functions and analytic continuation, Springer, New York, 1974. MR 486556

[DF] K. Davis and I. Foiaş, Operators with bounded characteristic function and their Junitary dilation, Acta Sci. Math. (Szeged) 32 (1971), 127139. MR 313845

[DH] R. G. Douglas and J. W. Helton, Inner dilations of analytic matrix functions and Darlington synthesis, Acta Sci. Math. (Szeged) 34 (1973), 6167. MR 322538

[DeW] P. DeWilde, Roomy scattering matrix synthesis, Univ. of California, Berkeley Tech. Report, 1971.

[DK] C. A. Desoer and E. S. Kuh, Basic circuit theory, McGrawHill, New York, 1969.

[DMP] R. G. Douglas, P. Muhly and C. Pearcy, Lifting commuting operators, Michigan Math. J. 13 (1968), 385393. MR 236752

[DV] P. DeWilde and T. Vandewalle, On the factorization of a nonsingular rational matrix, IEEE Trans. Circuits and Systems, CAS22 ( 1972), 637645. MR 392174

[EH] C. Earle and R. S. Hamilton, A fixed point theorem for holomorphic mappings, Global Analysis, Proc. Sympos. Pure Math., vol. 15, Amer. Math. Soc. Providence, R. I., 1970. MR 266009

[EP] A. V. Efimov and V. P. Potapov, Jexpanding functions and their role in the analytic theory of electrical circuits, Russian Math. Survey 28 (1973). MR 394287
 John W. Evans and J. William Helton, Applications of PickNevanlinna interpolation theory to retentionsolubility studies in the lungs, Math. Biosci. 63 (1983), no. 2, 215–240. MR 695728, https://doi.org/10.1016/00255564(82)900402

[Fa] R. M. Fano, Theoretical limitations on broadband matching of arbitrary impedances, J. Franklin Inst. 249 (1960), 5783; 139155.

[F] P. Fuhrman, On Hankel operator ranges meromorphic pseudocontinuations and factorization of operator analytic functions, J. London Math. Soc. (2) 13 (1975), 323327. MR 428099

[Fdl] I. I. Fedchin, Description of solutions of the tangential NevanlinnaPick problem, Doklady Akad. Nauk Armenian SSR 60 (1975), 3742. MR 385104

[Fd2] I. I. Fedchin, Tangential NevanlinnaPick problem with multiple points, Doklady Akad. Nauk Armenian SSR 61 (1975), 214218. MR 409824
 Ciprian Foiaş, Contractive intertwining dilations and waves in layered media, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, Helsinki, 1980, pp. 605–613. MR 562662

[GK] I. C. Gohberg and M. G. Krein, Systems of integral equations on a halfline with kernel depending on the difference of the arguments, Amer. Math. Soc. Transl. (2) 14 (1960). MR 113114
 J. William Helton, The distance of a function to 𝐻^{∞} in the Poincaré metric; electrical power transfer, J. Funct. Anal. 38 (1980), no. 2, 273–314. MR 587910, https://doi.org/10.1016/00221236(80)90066X
 J. William Helton, Orbit structure of the Möbius transformation semigroup acting on 𝐻^{∞} (broadband matching), Topics in functional analysis (essays dedicated to M. G. Kreĭn on the occasion of his 70th birthday), Adv. in Math. Suppl. Stud., vol. 3, Academic Press, New YorkLondon, 1978, pp. 129–157. MR 538017
 J. William Helton, Broadbanding: gain equalization directly from data, IEEE Trans. Circuits and Systems 28 (1981), no. 12, 1125–1137. MR 643026, https://doi.org/10.1109/TCS.1981.1084944

[H3E] J. William Helton, Broadbanding: gain equalization directly from data, An expanded version of [H3], available upon request.

[H4] J. William Helton, Operator theory and broadband matching, Proc. of the Allerton Conference on Circuits and Systems Theory ( 1976).

[H5] J. William Helton, A simple test to determine gainbandwidth limitations, IEEE International Conference on Circuit Systems (Phoenix, 1977), pp. 628631.

[H6] J. William Helton, Systems with infinite dimensional state space: the Hilbert space approach, Proc. IEEE 64 (1976), 145160. MR 416694

[Hs] H. Helson, Invariant subspaces, Academic Press, New York, 1964. MR 171178

[HPEE] HewlettPackard, E. E. Pac I programs for the HP67 and 97 calculators.

[HP2]HewlettPackard, Sparameter design, Application Note 154, April 1972.

[HR] J. H. C. van Heuven and T. Z. Rozzi, The invariant properties of a multivalue nport in a linear embedding, IEEE Trans. Circuit Theory 19 (1972).

[Htz] W. Hintzman, Best uniform approximation via annihilating measures, Bull. Amer. Math. Soc. 76 (1970), 10621066. MR 262747
 T. S. Ivanchenko, The NevanlinnaPick problem in the case of an indefinite metric, Dokl. Akad. Nauk Ukrain. SSR Ser. A 5 (1980), 8–13, 92 (Russian, with English summary). MR 579356

[Iv2]T. S. Ivanchenko, The Schur problem in the case of indefinite metrics, submitted to VINITI, July 31st, 1979, No. 286879.

[Iv3]T. S. Ivanchenko, NevanlinnaPick problem with simple poles, submitted to VINITI, June 24, 1980, No. 255880.
 Thomas Kailath, Linear systems, PrenticeHall, Inc., Englewood Cliffs, N.J., 1980. PrenticeHall Information and System Sciences Series. MR 569473

[KP] I. V. Kovalishyn and V. P. Potapov, Indefinite metric in the PickNevanlinna problem, Doklady Akad. Nauk Armenian SSR 59 (1974), 39.

[K] S. Kobayashi, Hyperbolic manifolds and holomorphic mappings, Dekker, New York, 1970. MR 277770

[KR] E. Kuh and R. A. Roher, Theory of linear active networks, HoldenDay, San Francisco, Calif., 1967.

[NF] B. SzNagy and C. Foiaş, Harmonic analysis of operators on Hilbert space, NorthHolland, Amsterdam, 1970. MR 275190

[Nul] A. A. Nudelman, On a new problem of the type of moment problem, Dokl. Akad. Nauk SSSR 233 (1977), 792795. MR 470632
 A. A. Nudel′man, A generalization of classical interpolation problems, Dokl. Akad. Nauk SSSR 256 (1981), no. 4, 790–793 (Russian). MR 601661

[P] V. P. Potapov, The multiplicative structure of Jcontractive matrix functions, Trudy Mos. Mat., Obsc. 4 (1955), 125136. (Russian) Amer. Math. Soc. Transl. 13 (1960), 131243. MR 76882

[R] R. Redheffer, On a certain linear fractional transformation, J. Math. Phys. 39 (1960), 269286. MR 141990

[RR] M. Rosenbloom and J. Rovnyak, An operator theoretic approach to theorems of the PickNevanlinna and Löwner types. I (to appear).

[S] D. Sarason, Generalized interpolation in H, Amer. Math. Soc. Transl. 127 (2) (1967), 180203. MR 208383

[SY] M. Saito and D. C. Youla, Interpolation with positive real functions, J. Franklin Inst. 284 (2) (1967), 77108. MR 255824

[VD] J. Vandewalle and P. DeWilde, On the irreducible cascade synthesis of a system with real rational transfer matrix, Trans. IEEE Circuit Systems, CAS 24 (1977), 481484. MR 465358

[W] R. Wohlers, Lumped and distributed passive networks, Academic Press, New York, 1969.

[W] R. Wohlers, Linear distributed and passive networks, Academic Press, New York and London, 1969.

[Yl] D. C. Youla, A new theory of broadband matchings, IEEE Trans. CT11 (1964), 3050.

[Y2] D. C. Youla, L. Kaplan and D. Stock, The analytic foundation of linear time invariant nports, Polytechnic Inst, of New York, Brooklyn, New York, P1BMRI Report 102862.

[ZF] G. Zames and B. A. Francis, Feedback and minimax sensitivity, Adv. Group for Aerospace Research and Development NATO Lecture Notes, 117, Multivariable Analysis and Design Techniques.
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Additional Information
DOI:
https://doi.org/10.1090/S027309791982150017