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Spectral approximations for Wiener-Hopf operators. II. (English) Zbl 0769.45001

[For part I see ibid. 2, No. 2, 237-261 (1990; Zbl 0706.45002).] Here the authors consider the connection between the spectral properties of a Wiener-Hopf operator \(Kf=\int^ \infty_ 0k(s-t)f(t)dt\) and finite- section operators \(K_ \beta f=\int^ \beta_ 0k(s-t)f(t)dt\), \(s\in(0,\beta)\), as \(\beta\to\infty\) in the space \(L_ 2(R^ 1_ +)\) with \(k\in L_ 1(R^ 1)\). In part I this problem was considered in the space \(L_ \infty(R^ 1_ +)\). They also show some conditions when \(\sigma(K_ \beta)\) is assymptotically dense in \(\sigma(K)\) as \(\beta\to\infty\).

MSC:

45C05 Eigenvalue problems for integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
45P05 Integral operators
47A10 Spectrum, resolvent
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators

Citations:

Zbl 0706.45002
Full Text: DOI

References:

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