Keywords
- Operator Function
- Toeplitz Operator
- Pole Function
- Partial Index
- Diagonal Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Refererences
Adamyan V. M., Arov D. Z., Krein M. G., Analytic properties of Schmidt pairs for a Hankel operator and the Schur-Takagi problem, Mat. Sbornik 86(128) (1971), 34–75 (Russian); English transl. in Mat. USSR Sbornik 15 (1971), 31–73.
Bercovici H., Foias C., Tannenbaum A., A spectral commutant lifting theorem, Trans. Amer. Math. Soc. (to appear).
Doyle J. C., Structured uncertainty in control system design, IEEE CDC Proceedings, Fort Lauderdale, Fl., 1985.
Helton J. W., Operator theory, analytic function, matrices and electrical engineering, CMBS Series No. 68, AMS, 1987.
Math Works Inc., μ-Analysis and Synthesis Toolbox for use with MATLAB, Palo Alto, 1990.
Nevanlinna R., Über beschränkte Funktionen die in gegebenen Punkten vorgeschriebene Werte annehmen, Ann. Acad. Sci. Fenn. Ser. A 13 (1919).
Pick G., Über die Beschränkungen analytischer Funktionen, welche durch vorgegebene Funktions werte bewirkt werden, Math. Ann. 77 (1916), 7–23.
Sarason D., Generalized approximation in H ∞, Trans. Amer. Math. Soc. 127 (1967), 179–203.
Schur I., Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind II, J. Reine Angew. Math. 148 (1918), 122–145.
References
Livshits M. S., On one class of linear operaoors in Hilbert space, Mat. Sbornik 19 (61) (1946), 236–260 (Russian)
Livshits M. S., Isometric operators with the same defect numbers, and quasi-unitary opretors, Mat. Sbornik 26 (1950), 247–264. (Russian)
Sz.-Nagy B., Foiaş C., Harmonic analysis of operators in Hilbert space, Akad. Kiadó, Budapest, 1970.
Adamyan V. M., Arov D. Z., Krein M. G., Infinite Hankel matrices and generalized Carathéodory-Fejér's and I. Schur's problems, Funktsion. Analiz i Prilozhen. 2 (1968), no. 4, 1–17. (Russian)
Adamyan V. M., Arov D. Z., Krein M. G., Infinite block-Hankel matrices and problems of extension related with them, Izv. Akad. Nauk Arm. SSR, ser. matem. 6 (1971), 181–206. (Russian)
Adamyan V. M., Non-degenerate unitary coupling of semi-unitary operators, Funkts. Anal. i. Prilozhen. 7 (1973) no. 4, 1–16 (Russian)
References
Arov D. Z., On the interpolation problem and Blaschke-Potapov product, Sketch of lectures, School on theory of operators on functional spaces, Minsk, 1982, pp. 14–15. (Russian)
Arov D. Z., Realization of matrix-valued functions according to Darlington, Izv. Akad. Nauk SSSR, ser. matem. 37 (1973), no. 6, 1299–1331.
Adamyan V. M., Arov D. Z., Krein M. G., Infinite Hankel matrices and generalized Carathéodory-Fejér's and I. Schur's problems, Funktsion. Analiz i Prilozhen. 2 (1968), no. 4, 1–17. (Russian)
Adamyan V. M., Arov D. Z., Krein M. G., Infinite block-Hankel matrices and problems of extension related with them, Izv. Akad. Nauk Arm. SSR, ser. matem. 6 (1971), no. 2-3, 87–112 (Russian)
Adamyan V. M., Non-degenerate unitary coupling of semi-unitary operators, Funkts. Anal. i. Prilozhen. 7 (1973), no. 4, 1–16. (Russian)
Arov D. Z., Simakova L. A., On boundary values of convergent sequence of J-contractive matrix-functions, Mat. Zameki 19 (1976), no. 4, 491–500. (Russian)
Potapov V. P., Multiplicative structure of J-nonexpanding matrix-functions, Trudy MMO 4 (1955), 125–236. (Russian)
Fedchina I. P., Tangential Nevanlinna-Pick problem with multiple points, Doklady Akad. Nauk Arm. SSSR 61 (1975), no. 4, 214–218. (Russian)
Krein M. G., General theorems on positive functionals, Some questions in the theory of moments, (by Ahiezer N. I., Krein M.), Kharkov, 1938, pp. 121–150 (Russian); English transl. vol. 2, Trans. Math. Mon., AMS, 1962, pp. 124–153.
Melamud E. Ya., Boundary Nevanlinna-Pick problem for J-expanding matrix-functions, Izvestiya VUZov, Matem. 6 (1984), 36–43 (Russian)
Reference
Sarason D., Exposed points in H 1. I, The Gohberg anniversary collection, vol. II (Calgary, AB, 1988), Operator Theory: Advances and Applications, vol. 41, Birkhäuser, Basel, 1989, pp. 485–496.
References
Potapov V. P, Multiplicative structure of J-nonexpanding matrix-functions, Trudy MMO 4 (1955), 125–236 (Russian)
Ginzburg Yu. P., Multiplicative representations and minorants of analytic operator-functions, Funktsion. Anal. i Prilozhen. 1 (1967), no. 3, 9–23 (Russian)
Brodskii M. S., Triangular and Jordan representations of linear operators, Nauka, Moscow, 1969. (Russian)
Brodskii M. S., Isaev, L. E., Triangular representations of dissipative operators with resolvent of exponential type, Doklady Akad. Nauk SSSR 188 (1969), no. 5, 971–973 (Russian); English transl. in Soviet Math. Dokl. 10 (1969).
Ginzburg Yu. P., On divisors and minorants of operator-functions of bounded type, Matem. Issledovaniya, Kishinëv 2 (1967), no. 4, 47–72 (Russian)
Mogilevskaya R. L., Nonmonotone multiplicative representations of bounded analytic operator-functions, Matem. Issledovaniya, Kishinëv 4 (1969), no. 4, 70–81. (Russian)
Kiselevskii G. E., Invariant subspaces of dissipative Volterra operators with nuclear imaginary part, Izv. Akad. Nauk SSSR, ser. matem. 32: (1968), no. 1, 3–23 (Russian)
Gohberg I. Ts., Krein M. G., Theory of Volterra operators on Hilbert spaces and its applications, Nauka, Moscow, 1967. (Russian)
Sakhnovich L. A., On dissipative Volterra operators, Mat. Sbornik 76 (118) (1968), no. 3, 323–343. (Russian)
References
Faddeev L., Integrable models in 1+1 dimensional quantum field theory, preprint, CEN-SACLAY, S. Ph. T./82/76.
Faddeev L. D., Reshetihin N. Yu., Hamiltonian structures for integrable fields theory models, Teor. Mat. Fiz. 57 (1983), no. 1, 323–343 (Russian)
References
Prössdorf S., Einige Klassen singulärer Gleichungen, Berlin, 1974.
Gohberg I. Ts., Fel'dman I. A., Convolution equations and projection methods of its solutions, Nauka, Moscow, 1971 (Russian)
Birkhoff G. D., Math. Ann. 74 (1913), 122–138.
Gohberg I. Ts., Leiterer J., General theorems on factorization of operator-functions with respect to contour. I. Holomorphic functions, Acta Sci. Math. 34 (1973), 103–120 (Russian); Gohberg I. Ts., Leiterer J., General theorems on factorization of operator-functions with respect to contour. II. Generalization, Acta Sci. Math. 35 (1973), 39–59 (Russian)
Gohberg I. Ts., Problem of factorization of operator-functions, Izv. Akad. Nauk SSSR, ser. matem. 28 (1964), no. 5, 1055–1082. (Russian)
Leiterer J., On factorization of matrices and operator-functions, Soobshch. Akad. Nauk Gruz. SSR 88 (1977), no. 3, 541–544. (Russian)
References
Arov D. Z., Darlington realization of matrix-valued functions, Izv. Akad. Nauk SSSR, ser. matem. 37 (1973), 1299–1331. (Russian)
Arov D. Z., γ-generating matrices, J-inner matrix functions and related extrapolation problems, deposited in Ukr. NIINTI (1986), no. 726-Uk. 86 (Russian)
Arov D. Z., On regular and singular J-inner matrix-functions and related extrapolation problems, Funkts. Anal. i Prilozh. 22 (1988), 57–59. (Russian)
Arov D. Z., γ-generating matrices, J-inner matrix-functions and related extrapolation problems, Teor. Funkts., Funktsion. Anal. i Prilozh. (Kharkov), part. I, 51 (1989), 61–67; part II, 52 (1989), 103–109; part III, 53 (1990), 57–64 (Russian); English transl. in J. Soviet Math. 52 (1990), no. 6, 3487–3491; 52, (1990), no. 5, 3421–3425; 58 (1992), no. 6, 532–537.
Arov D. Z., Regular J-inner matrix-functions and related continuation problems, Linear Operators in Function Spaces (G. Arsene et al., eds.), Operator Theory: Advances and Applications, vol. 43, Birkhäuser, Basel, 1990, pp. 63–87.
Dubovoj V. K., Fritzsche B., Kirstein B., Spectral association of matrix-valued Schur functions and related questions, submitted.
Fritzsche B., Fuchs S. H., Kirstein B., A Schur type matrix extension problem. VI, Math. Nachr. (to appear).
Potapov V. P., Fractional linear transformation of matrices, Studies in the theory of operators and their applications (V. A. Marčenko, ed.), Naukova Dumka, Kiev, 1979, pp. 75–97. (Russian).
References
[B] Borogovac M., Zeros of meromorphic matrix functions of the class N n×nK , Math. Nachr. (to appear).
[BL] Borogovac M., Langer H., A characterization of generalized zeros of negative type of matrix functions of class N n×nK , Operator theory: Adv. Appl. 28 (1988), 17–26.
[DLS] Dijksma A., Langer H., de Snoo H. S. V., Eigenvalues and pole functions of Hamiltonian systems with eigenvalue depending boundary conditions, submitted for publication.
[GS] Gohberg I. C., Sigal E. I., An operator generalization of the logarithmic residue theorem and the theorem of Rouché, Mat. Sb. 84 (1971), 607–629 (Russian); English, transl. in Math. USSR-Sb. 13 (1971), 603–625.
[L] Langer H., A characterization of generalized zeros of negative type of functions of the class NK, Operator Theory: Adv. Appl. 17 (1986), 201–212.
References
Apostol C., On a spectral equivalence of operators, Integral Equations and Operator Theory 32 (1988), 15–35.
Dunford N., Spectral operators, Pacific J. of Math. 4 (1954), 321–354.
Gohberg I., On some questions of spectral theory of finite-meromorphic operator-function, Izv. Arm. Akad. Nauk 6 (2–3) (1971), 160–181 (Russian)
Gohberg I., Problems on equivalence and on factorization, Informal note of a lecture given at the University of Marylad, College park, MD, February 5, 1975.
Gohberg I., Kaashoek M. A., Lay D., Spectral classification of operators and operator functions, Bull. Amer. Math. Soc. 82 (1976), 587–589.
Gohberg I., Kaashoek M. A., Lay D., Equivalence, linearization and decomposition of holomorphic operator functions, J. Funct. Analysis 28 (1978), 102–144.
Gohberg I., Sigal E. I., An operator generalization of the logarithmic residue theorem and Rouché's theorem, Mat. Sb. 84 (126) (1971) 607–629 (Russian); English transl. in Math. USSR Sb. 13 (1971), 603–625.
Gohberg I., Sigal E. I., Global factorization of a meromorphic operator-function and some of its applications, Mat. Issled. 6 (1971), no. 1, 63–82. (Russian)
Kaashoek M. A., van der Mee C., Rodman L., Analytic operator functions with compact spectrum. I. Spectral nodes, linearization and equivalence, Integral Equations and Operator Theory 4 (1981), 504–547.
Leiterer J., Local and global equivalence of meromorphic operator functions. I, Math. Nachr. 83 (1978), 7–29; II. Math. Nachr. 84 (1978), 145–170.
Rodman L., An introduction to operator polynomials, OT 38, Birkhäuser Verlag, Basel, 1989.
References
Leiterer J., Banach coherent analytic sheaves, Math. Nachr. 85 (1978), 91–109.
O'Brian N. R., Toledo D., Tong Y. L. L., A Grothendieck-Riemann-Roch formula for maps of complex manifolds, Math. Ann. 271 (1985), 493–526.
Putinar M., Une caractérisation des modules analytiques quasi-cohérents, C. R. Acad. Sci. Paris 309 (1989), no. I, 881–884.
Ramis J. L., Ruget G., Résidus et dualité, Invent. Math. 26 (1974), 89–131.
Taylor J. L., Analytic functional calculus for several commuting operators, Acta Math. 125 (1970), 1–38.
References
Szőkefalvi-Nagy B., Foiaş C., On contractions similar to isometries and Toeplitz operators, Ann. Acad. Scient. Fennicae, Ser. A. I. Mathematica 2 (1976), 553–564.
Arveson W., Interpolation problems in nest algebras, J. Func. Anal. 20 (1975), 208–233.
References
Tolokonnikov V. A., Estimates in the Carleson Corona theorem and finitely generated ideals of the algebra H ∞, Funktsion. Anal. i Prilozhen. 14 (1980), no. 4, 85–86 (Russian); English transl. in Funct. Anal. and its Appl. 14 (1980), no. 4.
Nikolskii N. K., Treatise on the Shift Operator, Nauka, Moscow, 1980 (Russian); English transl. Springer-Verlag, 1986.
Tolokonnikov V. A., Estimates in the Carleson Corona theorem, ideals of the algebra H ∞, a problem of Sz.-Nagy, Zapiski Nauchn. Semin. LOMI 113 (1981), 178–198 (Russian); English transl. in Soviet Math. J. 22 (1983), 1814–1828.
Uchiyama A., Corona theorems for countably many functions and estimates for their solutions, Preprint, University of California at Los Angeles, 1981.
Rosenblum, M., A corona theorem for countably many functions, Integral Equat. and Operator Theory 3 (1980), no. 2, 125–137.
Schubert C. F., The corona theorem as an operator theorem, Proc. Amer. Math. Soc., 69 (1978), no. 1, 73–76.
Treil S. R., Angles between coinvariant subspaces and an operator-valued corona problem. A question of Szőkefalvi-Nagy, Doklady Akad. Nauk SSSR 302 (1988), 1063–1067 (Russian); English transl. in Soviet Math. Doklady 38 (1989), 394–399.
Treil S. R., Geometric methods in spectral theory of vector-valued functions: some recent results, Toeplitz Operator and Spectral Function Theory (Nikolskii N. K., ed.), Operator Theory: Adv. and Appl., vol. 42, Birkhäuser Verlag, Basel, 1989, pp. 209–280.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag
About this chapter
Cite this chapter
Gohberg, I., Kaashoek, M.A. (1994). Holomorphic operator functions. In: Havin, V.P., Nikolski, N.K. (eds) Linear and Complex Analysis Problem Book 3. Lecture Notes in Mathematics, vol 1573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100205
Download citation
DOI: https://doi.org/10.1007/BFb0100205
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57870-3
Online ISBN: 978-3-540-48367-0
eBook Packages: Springer Book Archive
