Volterra systems of operators

Shmuel Kantorovitz

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The operational calculus and spectral properties of the operators S + ∑ζkVkkε{lunate} C) are investigated in the abstract setting of a so-called "Volterra system" {ifSk, Vk; k = 1,..., N}. This is motivated by the classical example Sk: f(x) → xkf(x), Vk:f(x) → fxk0 f(x1, ..., t,..., xN) dt in Lp([0, 1]N) (with S = ∑Sk), and by the known results for the case N = 1 (cf. S. Kantorovitz (Trans. Amer. Math. Soc. 132 (1968), 323-333; 146 (1969), 61-68; 156 (1971), 193-218)).

Original languageEnglish
Pages (from-to)135-150
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Jul 1988


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