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 FOK1CG ... remarked that this theorem was proved for compact groups in Theorem 1.1 , and that the only use XI.11.3 1151 NOTES ...
... remark inductively . 1 2 Let F1 and F2 be disjoint closed sets in R. We select an open set G1 in R such that FOK1CG ... remarked that this theorem was proved for compact groups in Theorem 1.1 , and that the only use XI.11.3 1151 NOTES ...
Page 1381
... remark following Definition 2.29 , the two linear functionals f → f ( 0 ) and † → ƒ ( 1 ) form a complete set of ... remarks following Definition 2.29 , the formal differential operator ( 1 / i ) ( d / dt ) , if considered to be ...
... remark following Definition 2.29 , the two linear functionals f → f ( 0 ) and † → ƒ ( 1 ) form a complete set of ... 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 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero