Volterra systems of operators

Shmuel Kantorovitz

doi:10.1016/0022-247x(88)90371-x

Volterra systems of operators

Shmuel Kantorovitz

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The operational calculus and spectral properties of the operators S + ∑ζ_kV_k (ζ_kε{lunate} C) are investigated in the abstract setting of a so-called "Volterra system" {ifS_k, V_k; k = 1,..., N}. This is motivated by the classical example S_k: f(x) → x_kf(x), V_k:f(x) → f^xk₀ f(x₁, ..., t,..., x_N) dt in L^p([0, 1]^N) (with S = ∑S_k), 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 language	English
Pages (from-to)	135-150
Number of pages	16
Journal	Journal of Mathematical Analysis and Applications
Volume	133
Issue number	1
DOIs	https://doi.org/10.1016/0022-247x(88)90371-x
State	Published - Jul 1988

Access to Document

10.1016/0022-247x(88)90371-x

Cite this

@article{ef1d53857c3240fabb791aed0f967774,

title = "Volterra systems of operators",

abstract = "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)).",

author = "Shmuel Kantorovitz",

year = "1988",

month = jul,

doi = "10.1016/0022-247x(88)90371-x",

language = "אנגלית",

volume = "133",

pages = "135--150",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

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 - https://www.scopus.com/pages/publications/38249027423

U2 - 10.1016/0022-247x(88)90371-x

DO - 10.1016/0022-247x(88)90371-x

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

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 -

Volterra systems of operators

Abstract

Access to Document

Other files and links

Fingerprint

Cite this