Linear Operators: Spectral theory |
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Page 1221
... continuous as functions on c , to L2 ( S ,, Σ , v ) . Let c = c ,. Then μ ( σo - c ) < ε , and it is evident from ... linear functionals y , ... , y - 1 in L2 ( Sm , E , v ) such that y ( W , ( , ) ) = d ;; , i = 1 , . . . , p - 1 . Define ...
... continuous as functions on c , to L2 ( S ,, Σ , v ) . Let c = c ,. Then μ ( σo - c ) < ε , and it is evident from ... linear functionals y , ... , y - 1 in L2 ( Sm , E , v ) such that y ( W , ( , ) ) = d ;; , i = 1 , . . . , p - 1 . Define ...
Page 1675
Nelson Dunford, Jacob T. Schwartz. - continuous linear functional on the Hilbert space HP ( C ) of norm at most A for each 0 < △ < b1 — a1 . It follows from Theorem IV.4.6 and Corollary IV.4.7 that there is a sequence 4 , of positive ...
Nelson Dunford, Jacob T. Schwartz. - continuous linear functional on the Hilbert space HP ( C ) of norm at most A for each 0 < △ < b1 — a1 . It follows from Theorem IV.4.6 and Corollary IV.4.7 that there is a sequence 4 , of positive ...
Page 1903
... continuous linear functionals , V.7.3 ( 436 ) non - existence in L ,, 0 < p < 1 , V.7.37 ( 438 ) Continuous functions . ( See also Abso- lutely continuous functions ) as a B - space , additional properties , IV.15 definition , IV.2.14 ...
... continuous linear functionals , V.7.3 ( 436 ) non - existence in L ,, 0 < p < 1 , V.7.37 ( 438 ) Continuous functions . ( See also Abso- lutely continuous functions ) as a B - space , additional properties , IV.15 definition , IV.2.14 ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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 deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero