Linear Operators: Spectral theory |
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Page 958
... disjoint sets in Bo whose union e is also in B 。. Let rn = en en + 10 . so that E ( r ) g → 0 for every g in L2 ( R ) and , by Lemma 5 , 0 ( g , y ( e , ) ) = 8E ( e ) E ( r ) g → 0 . This argument shows that the vector valued additive ...
... disjoint sets in Bo whose union e is also in B 。. Let rn = en en + 10 . so that E ( r ) g → 0 for every g in L2 ( R ) and , by Lemma 5 , 0 ( g , y ( e , ) ) = 8E ( e ) E ( r ) g → 0 . This argument shows that the vector valued additive ...
Page 959
... sets whose union is eb ,. Since uo is countably additive on Bo , Mo ( eb2 ) ... disjoint sequence in B. It is clear that μ ( Ua , ) ≥μ ( an ) , so that ... disjoint sets in Bo with eUe . Let ɛ > 0 be given , and let N be so large that Σ + ...
... sets whose union is eb ,. Since uo is countably additive on Bo , Mo ( eb2 ) ... disjoint sequence in B. It is clear that μ ( Ua , ) ≥μ ( an ) , so that ... disjoint sets in Bo with eUe . Let ɛ > 0 be given , and let N be so large that Σ + ...
Page 1187
... disjoint and their union is the whole plane . The resolvent set p ( T ) is open and the resolvent R ( λ ; T ) is an ... sets and that if a point 2 is not in any of these sets the inverse ( λI - T ) -1 must exist as an everywhere defined ...
... disjoint and their union is the whole plane . The resolvent set p ( T ) is open and the resolvent R ( λ ; T ) is an ... sets and that if a point 2 is not in any of these sets the inverse ( λI - T ) -1 must exist as an everywhere defined ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero