Linear Operators: Spectral theory |
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Page 931
... restriction of T to M is then represented as multiplication by z on a space of analytic functions . Applications are made to the restrictions of normal and unitary operators . Halmos , Lumer , and Schäffer [ 1 ] proved that the restriction ...
... restriction of T to M is then represented as multiplication by z on a space of analytic functions . Applications are made to the restrictions of normal and unitary operators . Halmos , Lumer , and Schäffer [ 1 ] proved that the restriction ...
Page 1218
... restriction of f to the complement of o is continuous . PROOF . If the restrictions fo , g | d are continuous then so is the restriction ( af + ẞg ) | σ ~ 8 and thus the class of measurable functions having the required property is a ...
... restriction of f to the complement of o is continuous . PROOF . If the restrictions fo , g | d are continuous then so is the restriction ( af + ẞg ) | σ ~ 8 and thus the class of measurable functions having the required property is a ...
Page 1613
... restriction of T1 ( t , X ) , the remaining part of the spectrum depends on the restriction chosen , and may lie in the residual spectrum and / or the point spectrum or in the resolvent set of the restricted operator . The main problem ...
... restriction of T1 ( t , X ) , the remaining part of the spectrum depends on the restriction chosen , and may lie in the residual spectrum and / or the point spectrum or in the resolvent set of the restricted operator . The main problem ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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(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 satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero