Spectral Theory of Families of Self-Adjoint Operators (Mathematics and its Applications, 57)

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