﻿﻿ ﻿ ﻿﻿ On self-adjoint and invertible linear relations generated by integral equations
 Conţinutul numărului revistei Articolul precedent Articolul urmator 401 2 Ultima descărcare din IBN: 2020-10-05 15:42 Căutarea după subiecte similare conform CZU 517.968.2+517.983 (1) Дифференциальные, интегральные и другие функциональные уравнения. Конечные разности. Вариационное исчисление. Функциональный анализ (242) SM ISO690:2012BRUK, Vladislav. On self-adjoint and invertible linear relations generated by integral equations. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2020, nr. 1(92), pp. 106-121. ISSN 1024-7696. EXPORT metadate: Google Scholar Crossref CERIF DataCiteDublin Core
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 1(92) / 2020 / ISSN 1024-7696 /ISSNe 2587-4322

 On self-adjoint and invertible linear relations generated by integral equations
CZU: 517.968.2+517.983
MSC 2010: 46G12, 45N05, 47A10.

Pag. 106-121

 Bruk Vladislav Yuri Gagarin State Technical University of Saratov Disponibil în IBN: 5 septembrie 2020

Rezumat

We define a minimal operator L0 generated by an integral equation with an operator measure and prove necessary and sufficient conditions for the operator L0 to be densely defined. In general, L 0 is a linear relation. We give a description of L 0 and establish that there exists a one-to-one correspondence between relations bL with the property L0 ⊂ bL⊂L 0 and relations  entering in boundary conditions. In this case we denote bL = L. We establish conditions under which linear relations L and  together have the following properties: a linear relation (l.r) is self-adjoint; l.r is closed; l.r is invertible, i.e., the inverse relation is an operator; l.r has the finitedimensional kernel; l.r is well-defined; the range of l.r is closed; the range of l.r is a closed subspace of the finite codimension; the range of l.r coincides with the space wholly; l.r is continuously invertible. We describe the spectrum of L and prove that families of linear relations L() and () are holomorphic together.

Cuvinte-cheie
integral equation, Hilbert space, boundary value problem, operator measure, linear relation, spectrum