Linear Operators: Spectral theory |
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Page 921
... perturbation in the strong operator topology and shall find it convenient to use the notation T T to mean that T → T in the strong operator 8 topology , i.e. , Tnx → Tx for every x X.7 921 PERTURBATION THEORY Perturbation Theory.
... perturbation in the strong operator topology and shall find it convenient to use the notation T T to mean that T → T in the strong operator 8 topology , i.e. , Tnx → Tx for every x X.7 921 PERTURBATION THEORY Perturbation Theory.
Page 1826
... perturbation method . J. Fac . Sci . Univ . Tokyo Sect . I. 6 , 145-226 ( 1951 ) . Perturbation theory of semi - bounded operators . Math . Ann . 125 , 435–447 ( 1953 ) . On the perturbation theory of closed linear operators . J. Math ...
... perturbation method . J. Fac . Sci . Univ . Tokyo Sect . I. 6 , 145-226 ( 1951 ) . Perturbation theory of semi - bounded operators . Math . Ann . 125 , 435–447 ( 1953 ) . On the perturbation theory of closed linear operators . J. Math ...
Page 1916
... Perturbation of bounded linear opera- tors , remarks on , ( 611-612 ) study of , VII.6 , VII.8.1–2 ( 597–598 ) , VII.8.4-5 ( 598 ) Perturbation of infinitesimal genera- tor of a semi - group , ( 630-639 ) Peter - Weyl theorem , XI.1.4 ...
... Perturbation of bounded linear opera- tors , remarks on , ( 611-612 ) study of , VII.6 , VII.8.1–2 ( 597–598 ) , VII.8.4-5 ( 598 ) Perturbation of infinitesimal genera- tor of a semi - group , ( 630-639 ) Peter - Weyl theorem , XI.1.4 ...
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