Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 889
... set in the domain of a spectral measure satisfying ( iii ) is necessarily an ... Borel sets in the plane and which satisfies ( iv ) for every de B. This ... Borel sets ( v ) ∞ ∞ Σ Ε ( δ ) α = E ( U8 ; ) x , x = H. i = 1 i = 1 A spectral ...
... set in the domain of a spectral measure satisfying ( iii ) is necessarily an ... Borel sets in the plane and which satisfies ( iv ) for every de B. This ... Borel sets ( v ) ∞ ∞ Σ Ε ( δ ) α = E ( U8 ; ) x , x = H. i = 1 i = 1 A spectral ...
Page 894
... set functions whose values on a set oЄ Σ are √ ̧g ( t ) E ( dt ) , E ( od ) , respectively . The integral Ss f ( s ) ... Borel set 8 in S and every pair x , x * with x = X , x * = X * . It follows ( II.3.15 ) that E ( 8 ) = 0 . Thus if E ...
... set functions whose values on a set oЄ Σ are √ ̧g ( t ) E ( dt ) , E ( od ) , respectively . The integral Ss f ( s ) ... Borel set 8 in S and every pair x , x * with x = X , x * = X * . It follows ( II.3.15 ) that E ( 8 ) = 0 . Thus if E ...
Page 913
... Borel set e . Using the Lebesgue decomposition theorem ( III.4.14 ) , let { e } be a sequence of Borel sets such that Σv , ( en ) · 0 , and such that if e is a Borel subset of the complement en of e , and Σv , ( e ) v , ( e ) 0. Let oo ...
... Borel set e . Using the Lebesgue decomposition theorem ( III.4.14 ) , let { e } be a sequence of Borel sets such that Σv , ( en ) · 0 , and such that if e is a Borel subset of the complement en of e , and Σv , ( e ) v , ( e ) 0. Let oo ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero