Resultant operators of a pair of analytic functions

Authors:
I. C. Gohberg and L. E. Lerer

Journal:
Proc. Amer. Math. Soc. **72** (1978), 65-73

MSC:
Primary 47B35

DOI:
https://doi.org/10.1090/S0002-9939-1978-0493487-8

MathSciNet review:
0493487

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Abstract: The well-known results on resultant of polynomials and its continuous analogue is generalized for some classes of analytic functions.

**[1]**I. C. Gohberg and I. A. Feldman,*Convolution equations and projection methods of their solution*, ``Nauka", Moscow, 1971; English transl., Transl. Math. Monographs, vol. 41, Amer. Math. Soc., Providence, R.I., 1974. MR**0355674 (50:8148)****[2]**I. C. Gohberg and G. Heinig,*Resultant matrix and its generalization*. I.*Resultant operator of matrix polynomials*, Acta Sci. Math. (Szeged)**37**(1975), Fase. 1 - 2, pp. 41-61. (Russian) MR**0380471 (52:1371)****[3]**-,*Resultant matrix and its generalization*. II:*Continual analog of resultant matrix*, Acta Math. Acad. Sci. Hungar.**28**(1976), 3-4, 189-209. (Russian) MR**0425652 (54:13606)****[4]**I. C. Gohberg and L. E. Lerer,*Resultants of matrix polynomials*, Bull. Amer. Math. Sci.**82**(1976), 565-567. MR**0407048 (53:10831)****[5]**M. G. Krein,*Integral equations on a half-line with kernel depending upon the difference of the arguments*, Uspehi Mat. Nauk**13**(1958), no. 5 (83), 2-120; English transl., Amer. Math. Soc. Transl. (2)**22**(1962), 163-288. MR**0102721 (21:1507)**

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DOI:
https://doi.org/10.1090/S0002-9939-1978-0493487-8

Keywords:
Common zeroes,
resultant matrix,
Wiener-Hopf pair operator,
factorization

Article copyright:
© Copyright 1978
American Mathematical Society