Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 1803
On some properties of completely additive set functions and their application to generalization of a theorem of Lebesgue . Mat . Sbornik N. S. 20 ( 62 ) , 317-329 ( 1947 ) . ( Russian , English summary ) Math . Rev. 9 , 19 ( 1948 ) .
On some properties of completely additive set functions and their application to generalization of a theorem of Lebesgue . Mat . Sbornik N. S. 20 ( 62 ) , 317-329 ( 1947 ) . ( Russian , English summary ) Math . Rev. 9 , 19 ( 1948 ) .
Page 1900
Almost periodic functions , definition , IV.2.25 ( 242 ) space of , additional properties , IV.15 ( 379 ) definition , IV.2.25 ( 242 ) remarks concerning , ( 386–387 ) study of , IV.7 . Almost uniform ( or u - uniform convergence ) ...
Almost periodic functions , definition , IV.2.25 ( 242 ) space of , additional properties , IV.15 ( 379 ) definition , IV.2.25 ( 242 ) remarks concerning , ( 386–387 ) study of , IV.7 . Almost uniform ( or u - uniform convergence ) ...
Page 1902
a properties , 1.3.12–14 ( 9 ) Cartesian product of topological spaces , 1.8 ( 31 ) Category theorem , of Baire , 1.6.9 ( 20 ) Cauchy integral formula , ( 227 ) for functions of an operator , in a finite dimensional space , VII.1.10 ...
a properties , 1.3.12–14 ( 9 ) Cartesian product of topological spaces , 1.8 ( 31 ) Category theorem , of Baire , 1.6.9 ( 20 ) Cauchy integral formula , ( 227 ) for functions of an operator , in a finite dimensional space , VII.1.10 ...
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additive adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero