Abstract
In the spaceL p (ℒ),p > 1, we consider the operatorA=aϕ +bSϕ +cPϕ +Tϕ, wherea(t), b(t), and c(t) are piecewise-continuous functions on the contour ℒ, T is a completely continuous operator, Pϕ=1/2πi∫ ϕ(τ) dτ/ℒ τ −t − 1, Sϕ=1/gpi∫ ϕ(τ) dτ/ℒ τ − i, ℒ is a closed convex Lyapunov contour having no rectilinear portions. We study the properties of the operator P and we show that the Noether property conditions and the index of the operator A do not depend on the term cP.
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Translated from Matematicheskie Zametki, Vol. 16, No. 4, pp. 529–535, October, 1974.
In conclusion the author expresses his thanks to G. S. Litvinchuk for his guidance of his work.
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Vasilevskii, N.L. On the properties of a class of integral operators in the space Lp . Mathematical Notes of the Academy of Sciences of the USSR 16, 905–909 (1974). https://doi.org/10.1007/BF01104253
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DOI: https://doi.org/10.1007/BF01104253