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Spectral asymptotic behavior of a class of integral operators (1974)

Laptev, A. A.

Springer

Mathematical notes 16 (1974), S. 1038-1043

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ISSN: 1573-8876

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Integral operators of the type $$(Tf)(x) = \int_0^1 {\frac{{x^\beta y^\gamma }}{{(x + y)^\alpha }}} f(y)dy,$$ the kernels of which have a singularity at a single point, are discussed. H. Widom's method and some of his results are used to show that, if α〉0, β, γ〉−1/2, ρ=β+γ−α+1〉0, then we have for the distribution function of the singular numbers of the operator, $$\mathop {\lim }\limits_{\varepsilon \to 0} N(\varepsilon ,T)ln^{ - 2} {\textstyle{1 \over \varepsilon }} = {\textstyle{1 \over {2\pi ^2 \varepsilon }}}.$$

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01149794

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