Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Bulletin of the American Mathematical Society
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
MathSciNet review: 656197
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • D. Z. Arov, Realization of matrix-valued functions according to Darlington, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973), 1299–1331 (Russian). MR 0357820 (50 #10287)
  • [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.
  • Gr. Arsene, Zoia Ceauşescu, and C. Foiaş, On intertwining dilations. VIII, J. Operator Theory 4 (1980), no. 1, 55–91. MR 587368 (82d:47013f)
  • T. Andô, On a pair of commutative contractions, Acta Sci. Math. (Szeged) 24 (1963), 88–90. MR 0155193 (27 #5132)
  • Joseph A. Ball, Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions, Integral Equations Operator Theory 6 (1983), no. 6, 804–840. MR 719106 (85k:30054), http://dx.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 (84j:94033)
  • [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).
  • Joseph A. Ball and J. William Helton, Subinvariants for analytic mappings on matrix balls, Analysis 1 (1981), no. 3, 217–226. MR 660718 (84d:32035)
  • [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.
  • Douglas N. Clark, On the spectra of bounded, Hermitian, Hankel matrices, Amer. J. Math. 90 (1968), 627–656. MR 0231112 (37 #6667)
  • William F. Donoghue Jr., Monotone matrix functions and analytic continuation, Springer-Verlag, New York, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 207. MR 0486556 (58 #6279)
  • Chandler Davis and Ciprian Foiaş, Operators with bounded characteristic function and their 𝐽-unitary dilation, Acta Sci. Math. (Szeged) 32 (1971), 127–139. MR 0313845 (47 #2398)
  • R. G. Douglas and J. William Helton, Inner dilations of analytic matrix functions and Darlington synthesis, Acta Sci. Math. (Szeged) 34 (1973), 61–67. MR 0322538 (48 #900)
  • [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.
  • R. G. Douglas, P. S. Muhly, and Carl Pearcy, Lifting commuting operators, Michigan Math. J. 15 (1968), 385–395. MR 0236752 (38 #5046)
  • Patrick Dewilde and Joos P. Vandewalle, On the factorization of a nonsingular rational matrix, IEEE Trans. Circuits and Systems CAS-22 (1975), no. 8, 637–645. MR 0392174 (52 #12991)
  • Clifford J. Earle and Richard S. Hamilton, A fixed point theorem for holomorphic mappings, Global Analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, Calif., (1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 61–65. MR 0266009 (42 #918)
  • A. V. Efimov and V. P. Potapov, 𝐽-expanding matrix-valued functions, and their role in the analytic theory of electrical circuits, Uspehi Mat. Nauk 28 (1973), no. 1(169), 65–130 (Russian). MR 0394287 (52 #15090)
  • John W. Evans and J. William Helton, Applications of Pick-Nevanlinna interpolation theory to retention-solubility studies in the lungs, Math. Biosci. 63 (1983), no. 2, 215–240. MR 695728 (84m:92005), http://dx.doi.org/10.1016/0025-5564(82)90040-2
  • [Fa] R. M. Fano, Theoretical limitations on broadband matching of arbitrary impedances, J. Franklin Inst. 249 (1960), 57-83; 139-155.
  • Paul A. Fuhrmann, On Hankel operator ranges, meromorphic pseudo-continuations and factorization of operator-valued analytic functions, J. London Math. Soc. (2) 13 (1976), no. 2, 323–327. MR 0428099 (55 #1128)
  • I. P. Fedčina, A description of the solutions of the Nevanlinna-Pick tangent problem, Akad. Nauk Armjan. SSR Dokl. 60 (1975), no. 1, 37–42 (Russian, with Armenian summary). MR 0385104 (52 #5974)
  • I. P. Fedčina, The tangential Nevanlinna-Pick problem with multiple points, Akad. Nauk Armjan. SSR Dokl. 61 (1975), no. 4, 214–218 (Russian, with Armenian summary). MR 0409824 (53 #13576)
  • 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 (82a:47002)
  • I. C. Gohberg and M. G. Kreĭn, Systems of integral equations on a half line with kernels depending on the difference of arguments, Amer. Math. Soc. Transl. (2) 14 (1960), 217–287. MR 0113114 (22 #3954)
  • 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 (82f:32035), http://dx.doi.org/10.1016/0022-1236(80)90066-X
  • 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 York, 1978, pp. 129–157. MR 538017 (81e:46019)
  • J. William Helton, Broadbanding: gain equalization directly from data, IEEE Trans. Circuits and Systems 28 (1981), no. 12, 1125–1137. MR 643026 (82m:94048), http://dx.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 gain-bandwidth limitations, IEEE International Conference on Circuit Systems (Phoenix, 1977), pp. 628-631.
  • J. William Helton, Systems with infinite-dimensional state space: the Hilbert space approach, Proc. IEEE 64 (1976), no. 1, 145–160. Recent trends in system theory. MR 0416694 (54 #4764)
  • Henry Helson, Lectures on invariant subspaces, Academic Press, New York, 1964. MR 0171178 (30 #1409)
  • [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).
  • William Hintzman, Best uniform approximations via annihilating measures, Bull. Amer. Math. Soc. 76 (1970), 1062–1066. MR 0262747 (41 #7352), http://dx.doi.org/10.1090/S0002-9904-1970-12560-5
  • T. S. Ivanchenko, The Nevanlinna-Pick 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 (84i:47056)
  • [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.
  • Thomas Kailath, Linear systems, Prentice-Hall Inc., Englewood Cliffs, N.J., 1980. Prentice-Hall Information and System Sciences Series. MR 569473 (82a:93001)
  • [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.
  • Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker Inc., New York, 1970. MR 0277770 (43 #3503)
  • [K-R] E. Kuh and R. A. Roher, Theory of linear active networks, Holden-Day, San Francisco, Calif., 1967.
  • Béla Sz.-Nagy and Ciprian Foiaș, Harmonic analysis of operators on Hilbert space, Translated from the French and revised, North-Holland Publishing Co., Amsterdam, 1970. MR 0275190 (43 #947)
  • A. A. Nudel′man, A new problem of the type of the moment problem, Dokl. Akad. Nauk SSSR 233 (1977), no. 5, 792–795 (Russian). MR 0470632 (57 #10379)
  • A. A. Nudel′man, A generalization of classical interpolation problems, Dokl. Akad. Nauk SSSR 256 (1981), no. 4, 790–793 (Russian). MR 601661 (82f:30033)
  • V. P. Potapov, The multiplicative structure of 𝐽-contractive matrix functions, Trudy Moskov. Mat. Obšč. 4 (1955), 125–236 (Russian). MR 0076882 (17,958f)
  • R. M. Redheffer, On a certain linear fractional transformation, J. Math. and Phys. 39 (1960), 269–286. MR 0141990 (25 #5385)
  • [R-R] M. Rosenbloom and J. Rovnyak, An operator theoretic approach to theorems of the Pick-Nevanlinna and Löwner types. I (to appear).
  • Donald Sarason, Generalized interpolation in 𝐻^{∞}, Trans. Amer. Math. Soc. 127 (1967), 179–203. MR 0208383 (34 #8193), http://dx.doi.org/10.1090/S0002-9947-1967-0208383-8
  • D. C. Youla and M. Saito, Interpolation with positive-real functions, J. Franklin Inst. 284 (1967), 77–108. MR 0255824 (41 #484)
  • Joos Vandewalle and Patrick Dewilde, On the irreducible cascade synthesis of a system with a real rational transfer matrix, IEEE Trans. Circuits and Systems CAS-24 (1977), no. 9, 481–494. MR 0465358 (57 #5260)
  • [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.

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1980): 35D55, 30E05, 32M15, 46J15, 47A45, 47A65, 47A68, 47B35, 47B38, 47B50, 94C05, 22E50

Retrieve articles in all journals with MSC (1980): 35D55, 30E05, 32M15, 46J15, 47A45, 47A65, 47A68, 47B35, 47B38, 47B50, 94C05, 22E50


Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1982-15001-7
PII: S 0273-0979(1982)15001-7