Spectral Theory of Families of Self-Adjoint Operators

Front Matter....Pages i-xvi
Introduction....Pages 1-5
Comments to the Introduction....Pages 5-5
Front Matter....Pages 7-7
Spectral Analysis of Countable Families of Commuting Self-Adjoint Operators (CSO)....Pages 7-40
Unitary Representations of Inductive Limits of Commutative Locally Compact Groups....Pages 41-66
Differential Operators with Constant Coefficients in Spaces of Functions of Infinitely Many Variables....Pages 67-85
Front Matter....Pages 87-88
Canonical Commutation Relations (CCR) of Systems with Countable Degrees of Freedom....Pages 89-114
Unitary Representations of the Group of Finite SU(2)-Currents on a Countable Set....Pages 115-123
Representations of the Group of Upper Triangular Matrices....Pages 124-144
A Class of Inductive Limits of Groups and their Representations....Pages 145-150
Front Matter....Pages 151-151
Anticommuting Self-Adjoint Operators....Pages 152-164
Finite and Countable Collections of Graded-Commuting Self-Adjoint Operators (GCSO)....Pages 165-191
Collections of Unbounded CSO ( A k ) and CSO ( B k ) Satisfying General Commutation Relations....Pages 192-220
Front Matter....Pages 221-221
 C *-Algebras U 0 ∞ and their Representations....Pages 222-230
Non-Commutative Random Sequences and Methods for their Construction....Pages 231-242
Back Matter....Pages 243-293