Linear Operators: Spectral theory |
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Page 1162
... obtained by Wermer [ 7 ] who determined the primary ideals in some of these algebras . Other results of a related nature have been obtained by Beurling [ 2 ] , [ 3 ] . Fredholm theory . Location of eigenvalues . The Fredholm theory of ...
... obtained by Wermer [ 7 ] who determined the primary ideals in some of these algebras . Other results of a related nature have been obtained by Beurling [ 2 ] , [ 3 ] . Fredholm theory . Location of eigenvalues . The Fredholm theory of ...
Page 1623
... obtained by imposition of the boundary condition B ( ƒ ) = ƒ ' ( 0 ) = 0 . Conversely , if the function q is assumed to have a continuous derivative , then the measure obtained from the spectral representa- tion ( cf. Theorem 5.13 ) of ...
... obtained by imposition of the boundary condition B ( ƒ ) = ƒ ' ( 0 ) = 0 . Conversely , if the function q is assumed to have a continuous derivative , then the measure obtained from the spectral representa- tion ( cf. Theorem 5.13 ) of ...
Page 1624
... obtained from the operator τ enjoy the property ∞ ∞ cos s√ cos t√Ãμ ( dλ ) = 0 , st . Making use of these relations , Gelfand and Levitan attempt to reconstruct the functions f ( t , 2 ) by " orthogonalizing " the functions cos t ...
... obtained from the operator τ enjoy the property ∞ ∞ cos s√ cos t√Ãμ ( dλ ) = 0 , st . Making use of these relations , Gelfand and Levitan attempt to reconstruct the functions f ( t , 2 ) by " orthogonalizing " the functions cos t ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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