LINEAR INTEGRAL VOLTERRA EQUATION OF THE FIRST KIND IN THE BANACH SPACE
Authors:
3.
Voronezh State University of Forestry and Technologies named after G.F. Morozov
Type:
Article
Pages:
from 113
to 114
Status:
Published
Received:
29.08.2014
Accepted:
09.10.2014
Published:
09.10.2014
Language:
Russian
Keywords:
integral equation, Banach space, operator pencil, spectrum
Abstract (English):
We construct a multiparametric set of solutions to a singular Volterra integral equation of the first kind with a sufficiently smooth kernel in the space of integrable functions whose values belong to a Banach space.
We construct a multiparametric set of solutions to a singular Volterra integral equation of the first kind with a sufficiently smooth kernel in the space of integrable functions whose values belong to a Banach space.
Keywords:
integral equation, Banach space, operator pencil, spectrum
integral equation, Banach space, operator pencil, spectrum
1.Постановка задачи. Формулировка основного результата
В вещественном банаховом пространстве зафиксируем норму . Эта норма индуцирует в пространстве всех линейных ограниченных операторов на операторную норму.
1. Sapronov, I. V. Uravnenie Vol´terra s osobennost´yu v banakhovom prostranstve / I. V. Sapronov. Izv. vuzov. Matematika. 2007. № 11 S. 45-55.
2. Sapronov, I. V. Mnogoparametricheskoe semeystvo resheniy integral´nogo uravneniya Vol´terra s osobennost´yu v banakhovom prostranstve / I. V. Sapronov. Izv. vuzov. Matematika. 2011. № 1 S. 59-71.
