Linear Operators: Spectral theory |
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Page 1582
... theory of integration and by the use of some arguments of heuristic rather than strictly logical character ( which were not made rigorous until 1905 ) , nevertheless already contains practically all the characteristic features of the theory ...
... theory of integration and by the use of some arguments of heuristic rather than strictly logical character ( which were not made rigorous until 1905 ) , nevertheless already contains practically all the characteristic features of the theory ...
Page 1585
... theory of differential operators of second order assumes a physically significant role . Thus the physicists of the time were naturally led to interest themselves in the theory of Weyl . But , while many of the useful insights of the ...
... theory of differential operators of second order assumes a physically significant role . Thus the physicists of the time were naturally led to interest themselves in the theory of Weyl . But , while many of the useful insights of the ...
Page 1628
... theory can be found in Levitan [ 1 ] . An approach to the study of differential operators in a Banach space of a more complex character than Hilbert space has been carried out by Feller [ 1 ] through [ 7 ] ) in his investigations of the ...
... theory can be found in Levitan [ 1 ] . An approach to the study of differential operators in a Banach space of a more complex character than Hilbert space has been carried out by Feller [ 1 ] through [ 7 ] ) in his investigations of the ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Copyright | |
59 other sections not shown
Common terms and phrases
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