The Resultant Matrix and its Generalizations. II. The Continual Analogue of the Resultant Operator

  • Israel Gohberg
  • Georg Heinig
Part of the Operator Theory: Advances and Applications book series (OT, volume 206)


Let A(λ) and B(λ) (λ ∈ ℂ1) be entire functions of the form \( \mathcal{A}(\lambda ) = a_0 + \int_0^\tau {a(t)e^{i\lambda t} dt} , \mathcal{B}(\lambda ) = b_0 + \int_{ - \tau }^0 {b(t)e^{i\lambda t} dt} , \) where a 0, b 0 ∈ ℂ1, a(t) ∈ L 1(0, τ), b(t) ∈ L 1(−τ, 0), and τ is some positive number.


Entire Function Vector Function Resultant Operator Operator Function Matrix 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    I.C. Gohberg and G. Heinig, The resultant matrix and its generalizations. I. The resultant operator for matrix polynomials. Acta Sci. Math. (Szeged) 37 (1975), 41–61 (in Russian). English translation: this volume. MR0380471 (52 #1371), Zbl 0298.15013.MATHMathSciNetGoogle Scholar
  2. [2]
    I.C. Gohberg and M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert space. Nauka, Moscow, 1965 (in Russian). MR0220070 (36 #3137), Zbl 0138.07803. English translation: Introduction to the Theory of Linear Nonselfadjoint Operators. Amer. Math. Soc., Providence, R.I. 1969. MR0246142 (39 #7447), Zbl 0181.13504. French translation: Introduction à la Théorie des Opérateurs Linéaires non Auto-Adjoints Dans un Espace Hilbertien. Dunod, Paris, 1971. MR0350445 (50 #2937).Google Scholar
  3. [3]
    I.C. Gohberg and E.I. Sigal, An operator generalization of the logarithmic residue theorem and the theorem of Rouché. Matem. Sbornik, New Ser. 84(126) (1971), 607 629 (in Russian). English translation: Math. USSR Sbornik 13 (1971), 603–625. MR0313856 (47 #2409), Zbl 0254.47046.MathSciNetGoogle Scholar
  4. [4]
    I.C. Gohberg and A.A. Semencul, The inversion of finite Toeplitz matrices and their continual analogues. Matem. Issled. 7 (1972), no. 2(24), 201–223 (in Russian). MR0353038 (50 #5524), Zbl 0288.15004.MATHMathSciNetGoogle Scholar
  5. [5]
    I.C. Gohberg and G. Heinig, Matrix integral operators on a finite interval with kernels depending on the difference of the arguments. Rev. Roumaine Math. Pures Appl. 20 (1975), 55–73 (in Russian). English translation: this volume. MR0380495 (52 #1395), Zbl 0327.45009.MathSciNetGoogle Scholar
  6. [6]
    M.G. Krein and M.A. Naimark, The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations. Khar’kov, 1936 (in Russian). English translation: Linear and Multilinear Algebra 10 (1981), no. 4, 265–308. MR0638124 (84i:12016), Zbl 0584.12018.Google Scholar
  7. [7]
    F.I. Lander, The Bezoutian and the inversion of Hankel and Toeplitz matrices. Matem. Issled. 9 (1974), no. 2(32), 69-87 (in Russian). MR0437559 (55 #10483), Zbl 0331.15017.Google Scholar
  8. [8]
    M.G. Krein, Distribution of roots of polynomials orthogonal on the unit circle with respect to a sign-alternating weight. Teor. Funkts., Funkts. Anal. Prilozh. (Khar’kov) 2 (1966), 131–137 (in Russian). MR0201702 (34 #1584), Zbl 0257.30002.MATHMathSciNetGoogle Scholar

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Israel Gohberg
  • Georg Heinig

There are no affiliations available

Personalised recommendations