Linear Operators: Spectral theory |
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Page 930
... problem is related to the problem of spectral synthesis to be discussed in Section XI.4 . A similar problem was discussed by Beurling [ 4 ] , who was able to find all of the closed invariant subspaces for the operator of multiplication ...
... problem is related to the problem of spectral synthesis to be discussed in Section XI.4 . A similar problem was discussed by Beurling [ 4 ] , who was able to find all of the closed invariant subspaces for the operator of multiplication ...
Page 1250
... problem proposed and solved by Stieltjes is to find a mass distribution μ on [ 0 , which has prescribed moments . The Hamburger moment problem is similar to that of Stieltjes and differs from it by using the whole real axis ...
... problem proposed and solved by Stieltjes is to find a mass distribution μ on [ 0 , which has prescribed moments . The Hamburger moment problem is similar to that of Stieltjes and differs from it by using the whole real axis ...
Page 1270
... problem of determining whether a given symmetric operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed . If the answer to this problem is affirmative , it is important ...
... problem of determining whether a given symmetric operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed . If the answer to this problem is affirmative , it is important ...
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