TY - JOUR
T1 - Volterra systems of operators
AU - Kantorovitz, Shmuel
PY - 1988/7
Y1 - 1988/7
N2 - The operational calculus and spectral properties of the operators S + ∑ζkVk (ζkε{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)).
AB - The operational calculus and spectral properties of the operators S + ∑ζkVk (ζkε{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)).
UR - http://www.scopus.com/inward/record.url?scp=38249027423&partnerID=8YFLogxK
U2 - 10.1016/0022-247X(88)90371-X
DO - 10.1016/0022-247X(88)90371-X
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SN - 0022-247X
VL - 133
SP - 135
EP - 150
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -