Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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For an account of the representations of the group A ( n ) of all permutations of n objects , see Littlewood , The theory of group characters and matrix representations of groups , Oxford , Clarendon Press , 1950.
For an account of the representations of the group A ( n ) of all permutations of n objects , see Littlewood , The theory of group characters and matrix representations of groups , Oxford , Clarendon Press , 1950.
Page 1843
Markoff chains , Wiener integrals , and quantum theory . Comm . Pure Appl . Math . 5 , 415–453 ( 1952 ) . Moore , E. H. 1 . Introduction to a form of general analysis . The New Haven Math . Colloquium of the Amer . Math . Soc . , 1906 .
Markoff chains , Wiener integrals , and quantum theory . Comm . Pure Appl . Math . 5 , 415–453 ( 1952 ) . Moore , E. H. 1 . Introduction to a form of general analysis . The New Haven Math . Colloquium of the Amer . Math . Soc . , 1906 .
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Functional analysis and the general theory of functions . Reale Accademia d'Italia , Fondezione Allesandro Volta . Atti dei Convegni . 9 , 339-372 ( 1939 ) , Rome 1943 ( Spanish ) . 611-616 ( 1953 ) . Rudin , W. 1 . REFERENCES 1855.
Functional analysis and the general theory of functions . Reale Accademia d'Italia , Fondezione Allesandro Volta . Atti dei Convegni . 9 , 339-372 ( 1939 ) , Rome 1943 ( Spanish ) . 611-616 ( 1953 ) . Rudin , W. 1 . REFERENCES 1855.
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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