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Korotkov, V. B.

Systems of integral equations. (English) Zbl 0621.45003

Sib. Math. J. 27, 406-416 (1986).
Translation from Sib. Mat. Zh. 27, No.3(157), 121-133 (Russian) (1986; Zbl 0607.45001).

Cited in 1 Document

MSC:

45F05 Systems of nonsingular linear integral equations
45P05 Integral operators
45C05 Eigenvalue problems for integral equations
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators

Keywords:

reduction; systems; compact operator; Hilbert-Schmidt matrix-kernel; eigenvalue; Carleman matrix-kernel; resolvent; linear integral operator; Hermitian

Citations:

Zbl 0607.45001
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Full Text: DOI

References:

[1] V. B. Korotkov and V. D. Stepanov, ?On some properties of convolution integral operators,? in: Application of Methods of Functional Analysis to Problems of Mathematical Physics and Numerical Mathematics [in Russian], IM SO AN SSSR, Novosibirsk (1979), pp. 64-68. · Zbl 0472.47027
[2] V. B. Korotkov, ?On regular and compact factorizations of integral operators in Lp,? Mat. Zametki,32, No. 5, 601-606 (1982). · Zbl 0537.45013
[3] V. B. Korotkov, ?Carleman operators in spaces of abstract functions. I, II,? Sib. Mat. Zh.,12, No. 4, 727-747 (1971). · Zbl 0229.47036
[4] M. Misra, D. Speiser, and G. Targonski, ?Integral operators in the theory of scattering,? Helv. Phys. Acta,36, No. 7, 963-980 (1963). · Zbl 0134.45803
[5] T. Carleman, Sur les équations intégrales singulières a noyau réel et symétrique, A.-B. Lundequistska Bokhandeln, Uppsala (1923). · JFM 49.0272.01
[6] N. I. Akhiezer, ?Integral operators with Carleman kernels,? Usp. Mat. Nauk,2, No. 5, 93-132 (1947).
[7] N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, Ungar Press. · Zbl 0098.30702
[8] V. B. Korotkov, ?On integral equations of the first and third kind,? in: Mathematical Analysis and Adjacent Problems of Mathematics [in Russian], Nauka, Novosibirsk (1978), pp. 61-68.
[9] V. B. Korotkov, ?On general integral equations of the third kind,? Differents. Uravn.,15, No. 6, 1097-1105 (1979). · Zbl 0427.45001
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