Ostrovskyi V. Representations of operator relations

Українська версія

Thesis for the degree of Doctor of Science (DSc)

State registration number

0505U000019

Thesis Registration Form

0505U000019.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

28-12-2004

Specialized Academic Board

Д 26.206.01

The Institute of Mathematics of NASU

Essay

The thesis is devoted to the study of the structure of collections of bounded and unbounded operators in a Hilbert space satisfying certain algebraic relations. Classification is given for quadratic relations connecting a pair of self-adjoint operators. For non-degenerated cases, the structure of solutions is given. For the class of operator relations arising from dynamical system, the technique is developed to study their representations. The results are applied to the description of representations of important examples and classes of operator relations. In particular, commutative model for representations of the Cuntz algebras is constructed.

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Files

autoref.pdf

diss1.pdf

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