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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Non-Euclidean functional analysis and electronics


Author: J. William Helton
Journal: Bull. Amer. Math. Soc. 7 (1982), 1-64
MSC (1980): Primary 35D55, 30E05, 32M15, 46J15, 47A45, 47A65, 47A68, 47B35, 47B38, 47B50, 94C05; Secondary 22E50
DOI: https://doi.org/10.1090/S0273-0979-1982-15001-7
MathSciNet review: 656197
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  • [A] D. Z. Arov, Darlington realization of matrix-valued functions, Izv. Akad. Nauk SSSR Ser Mat. 37 (1973), 1299-1331; English transl. in Math. USSR Izv. 7 (1973). MR 357820
  • [A-A-Kl] V. M. Adamajan, D. Z. Arov and M. G. Krein, Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem, Math. USSR-Sb. 15 (1971), 31-73.
  • [A-A-K2] 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), 133-156.
  • [A-C-F] Gr. Arsene, Z. Ceausescu and C. Foiaş, On intertwining dilations. VIII, J. Operator Theory 4 (1980), 55-91. MR 587368
  • [An] T. Ando, On a pair of commutative contractions, Acta Sci. Math. (Szeged) 24 (1963), 88-90. MR 155193
  • [B] J. Ball, Interpolation problems of Pick-Nevanlinna and Löwner types for meromorphic matrix functions (preprint available). MR 719106
  • [B-Hl] 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
  • [B-H2] 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).
  • [B-H3] J. A. Ball and J. W. Helton, Subinvariants for analytic mappings on matrix balls, J. Anal. and Appl. (to appear). MR 660718
  • [B-H4] J. A. Ball and J. W. Helton, A Beurling-Lax theorem for the Lie group U (m, n) which contains most classical interpolation theory, J. Operator Theory (to appear).
  • [B-H5] 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.
  • [C-K] Y. T. Chan and E. Kuh, A general matching theory and its applications to tunnel a diode amplifier, IEEE Trans. C.T. 13 (1966), 6-18.
  • [C-L] L. Chua and Pen-Min-Lin, Computer aided analysis of electronic circuits: Algorithms and computational techniques, Prentice-Hall, Englewood Cliffs, New Jersey, 1975.
  • [C] D. Clark, On the spectra of bounded hermitian Hankel matrices, Amer. J. Math. 90 (1968), 627-656. MR 231112
  • [D] W. F. Donoghue, Monotone matrix functions and analytic continuation, Springer, New York, 1974. MR 486556
  • [D-F] K. Davis and I. Foiaş, Operators with bounded characteristic function and their J-unitary dilation, Acta Sci. Math. (Szeged) 32 (1971), 127-139. MR 313845
  • [D-H] R. G. Douglas and J. W. Helton, Inner dilations of analytic matrix functions and Darlington synthesis, Acta Sci. Math. (Szeged) 34 (1973), 61-67. MR 322538
  • [DeW] P. DeWilde, Roomy scattering matrix synthesis, Univ. of California, Berkeley Tech. Report, 1971.
  • [D-K] C. A. Desoer and E. S. Kuh, Basic circuit theory, McGraw-Hill, New York, 1969.
  • [D-M-P] R. G. Douglas, P. Muhly and C. Pearcy, Lifting commuting operators, Michigan Math. J. 13 (1968), 385-393. MR 236752
  • [D-V] P. DeWilde and T. Vandewalle, On the factorization of a nonsingular rational matrix, IEEE Trans. Circuits and Systems, CAS-22 ( 1972), 637-645. MR 392174
  • [E-H] 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
  • [E-P] A. V. Efimov and V. P. Potapov, J-expanding functions and their role in the analytic theory of electrical circuits, Russian Math. Survey 28 (1973). MR 394287
  • [E-H] J. Evans and J. W. Helton, Applications of Pick-Nevanlinna interpolation theory to retention-solubility 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), 57-83; 139-155.
  • [F] P. Fuhrman, On Hankel operator ranges meromorphic pseudo-continuations and factorization of operator analytic functions, J. London Math. Soc. (2) 13 (1975), 323-327. MR 428099
  • [Fdl] I. I. Fedchin, Description of solutions of the tangential Nevanlinna-Pick problem, Doklady Akad. Nauk Armenian SSR 60 (1975), 37-42. MR 385104
  • [Fd2] I. I. Fedchin, Tangential Nevanlinna-Pick problem with multiple points, Doklady Akad. Nauk Armenian SSR 61 (1975), 214-218. 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. 605-613. MR 562662
  • [G-K] I. C. Gohberg and M. G. Krein, Systems of integral equations on a half-line 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), 273-314. 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. 129-197. 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 gain-bandwidth limitations, IEEE International Conference on Circuit Systems (Phoenix, 1977), pp. 628-631.
  • [H6] J. William Helton, Systems with infinite dimensional state space: the Hilbert space approach, Proc. IEEE 64 (1976), 145-160. MR 416694
  • [Hs] H. Helson, Invariant subspaces, Academic Press, New York, 1964. MR 171178
  • [HPEE] Hewlett-Packard, E. E. Pac I programs for the HP-67 and 97 calculators.
  • [HP2]Hewlett-Packard, S-parameter design, Application Note 154, April 1972.
  • [H-R] J. H. C. van Heuven and T. Z. Rozzi, The invariant properties of a multivalue n-port 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), 1062-1066. MR 262747
  • [Ivl] T. S. Ivanchenko, The Nevanlinna-Pick problem in the case of indefinite metrics, Doklady Akad. Nauk Ukrainian SSR (1980), 8-13. MR 579356
  • [Iv2]T. S. Ivanchenko, The Schur problem in the case of indefinite metrics, submitted to VINITI, July 31st, 1979, No. 2868-79.
  • [Iv3]T. S. Ivanchenko, Nevanlinna-Pick problem with simple poles, submitted to VINITI, June 24, 1980, No. 2558-80.
  • [K] T. Kailath, Linear systems, Princeton-Hall, Englewood Cliffs, New Jersey, 1980. MR 569473
  • [K-P] I. V. Kovalishyn and V. P. Potapov, Indefinite metric in the Pick-Nevanlinna problem, Doklady Akad. Nauk Armenian SSR 59 (1974), 3-9.
  • [K] S. Kobayashi, Hyperbolic manifolds and holomorphic mappings, Dekker, New York, 1970. MR 277770
  • [K-R] E. Kuh and R. A. Roher, Theory of linear active networks, Holden-Day, San Francisco, Calif., 1967.
  • [N-F] B. Sz-Nagy and C. Foiaş, Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam, 1970. MR 275190
  • [Nul] A. A. Nudelman, On a new problem of the type of moment problem, Dokl. Akad. Nauk SSSR 233 (1977), 792-795. MR 470632
  • [Nu2] A. A. Nudelman, On a generalization of classical interpolation problems, Dokl. Akad. Nauk SSSR 256, (1981), 790-793. MR 601661
  • [P] V. P. Potapov, The multiplicative structure of J-contractive matrix functions, Trudy Mos. Mat., Obsc. 4 (1955), 125-136. (Russian) Amer. Math. Soc. Transl. 13 (1960), 131-243. MR 76882
  • [R] R. Redheffer, On a certain linear fractional transformation, J. Math. Phys. 39 (1960), 269-286. MR 141990
  • [R-R] M. Rosenbloom and J. Rovnyak, An operator theoretic approach to theorems of the Pick-Nevanlinna and Löwner types. I (to appear).
  • [S] D. Sarason, Generalized interpolation in H, Amer. Math. Soc. Transl. 127 (2) (1967), 180-203. MR 208383
  • [S-Y] M. Saito and D. C. Youla, Interpolation with positive real functions, J. Franklin Inst. 284 (2) (1967), 77-108. MR 255824
  • [V-D] 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), 481-484. 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. CT-11 (1964), 30-50.
  • [Y2] D. C. Youla, L. Kaplan and D. Stock, The analytic foundation of linear time invariant n-ports, Polytechnic Inst, of New York, Brooklyn, New York, P1B-MRI Report 1028-62.
  • [Z-F] 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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DOI: https://doi.org/10.1090/S0273-0979-1982-15001-7

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