Linear Operators: Spectral theory |
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Page 1151
... remark inductively . 1 2 Let F1 and F2 be disjoint closed sets in R. We select an open set G1 in R such that F1111 ... remarked that this theorem was proved for compact groups in Theorem 1.1 , and that the only use XI.11.3 1151 NOTES AND ...
... remark inductively . 1 2 Let F1 and F2 be disjoint closed sets in R. We select an open set G1 in R such that F1111 ... remarked that this theorem was proved for compact groups in Theorem 1.1 , and that the only use XI.11.3 1151 NOTES AND ...
Page 1381
... remark T1 following Definition 2.29 , the two linear functionals ƒ → f ( 0 ) and f → f ( 1 ) form a complete set ... remarks following Definition 2.29 , the formal differential operator ( 1 / i ) ( d / dt ) , if considered to be ...
... remark T1 following Definition 2.29 , the two linear functionals ƒ → f ( 0 ) and f → f ( 1 ) form a complete set ... remarks following Definition 2.29 , the formal differential operator ( 1 / i ) ( d / dt ) , if considered to be ...
Page 1900
... remarks concerning , ( 383 ) Ascoli - Arzelà theorem , on compact- ness of continuous functions , IV.6.7 ( 266 ) remarks concerning , ( 382 ) Atom , in a measure space , IV.9.6 ( 308 ) Automorphisms , in groups , ( 35 ) B B - algebra ...
... remarks concerning , ( 383 ) Ascoli - Arzelà theorem , on compact- ness of continuous functions , IV.6.7 ( 266 ) remarks concerning , ( 382 ) Atom , in a measure space , IV.9.6 ( 308 ) Automorphisms , in groups , ( 35 ) B B - algebra ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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(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 satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero