On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. II. Abstract Theory

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2006
• Main Author: Khrabustovsky, V.I.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2006
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/106621
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. II. Abstract Theory / V.I. Khrabustovsky // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 3. — С. 299-317. — Бібліогр.: 35 назв. — англ.

Special maximal semi-definite subspaces (maximal dissipative and accumulative relations) are considered. Particular cases of those arise in studying boundary problems for systems mentioned in the title. We provide a description of such subspaces and list their properties. A criterion is found that condition of semi-definiteness of sum of indefinite quadratic forms reduces to semi-definiteness of each of the summand forms, i.e it is separated. In the case when the forms depend on a parameter λ (e.g., a spectral parameter) within a domain Λ is in C, a condition is found under which separation of the semi-definiteness property at a single λ implies its separation for all λ.