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
Fulltext PDF Free Access
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.

[ACF] Gr. Arsene, Z. Ceausescu and C. Foiaş, On intertwining dilations. VIII, J. Operator Theory 4 (1980), 5591. MR 587368

[An] T. Ando, On a pair of commutative contractions, Acta Sci. Math. (Szeged) 24 (1963), 8890. MR 155193

[B] J. Ball, Interpolation problems of PickNevanlinna and Löwner types for meromorphic matrix functions (preprint available). MR 719106

[BHl] J. A. Ball and J. W. Helton, Lie groups over the field of rational functions, signed spectral factorization, signed interpolation, and amplifier designs, J. Operator Theory (to appear). 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).

[BH3] J. A. Ball and J. W. Helton, Subinvariants for analytic mappings on matrix balls, J. Anal. and Appl. (to appear). MR 660718

[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

[EH] J. Evans and J. W. Helton, Applications of PickNevanlinna interpolation theory to retentionsolubility studies in the lungs (preprint available). MR 695728

[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

[Fo] C. Foiaş, Contractive intertwining dilations and waves in layered media, Proc. Internat. Congr. Math. (Helsinki, 1978), Vol. 1, Acad. Sci. Fenn., Helsinki, 1980, pp. 605613. 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

[H1] J. William Helton, The distance from a function to H, J. Funct. Anal. 38 (1980), 273314. MR 587910

[H2] J. William Helton, Orbit structure of the Möbius transformation semigroup action on H (broadband matching), Advances in Math. Suppl. Studies, vol. 3, Academic Press, New York, 1978, pp. 129197. MR 538017

[H3] J. William Helton, Broadbanding: gain equalization directly from data, IEEE Trans, on Circuits and Systems 28 (1981). MR 643026

[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

[Ivl] T. S. Ivanchenko, The NevanlinnaPick problem in the case of indefinite metrics, Doklady Akad. Nauk Ukrainian SSR (1980), 813. 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.

[K] T. Kailath, Linear systems, PrincetonHall, Englewood Cliffs, New Jersey, 1980. 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

[Nu2] A. A. Nudelman, On a generalization of classical interpolation problems, Dokl. Akad. Nauk SSSR 256, (1981), 790793. 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