Linear Operators: Spectral theory |
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Page 1092
... finite number N of non - zero eigenvalues , we write λ „ ( T ) = 0 , n > N ) . Then , for each positive integer m ... finite- dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain ...
... finite number N of non - zero eigenvalues , we write λ „ ( T ) = 0 , n > N ) . Then , for each positive integer m ... finite- dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain ...
Page 1147
... finite set , then any complete set of representations of G is countable . A complete set of representations of a finite group is finite . DEFINITION : A class function on a compact group G is an element f of L2 ( G ) such that f ( h ) ...
... finite set , then any complete set of representations of G is countable . A complete set of representations of a finite group is finite . DEFINITION : A class function on a compact group G is an element f of L2 ( G ) such that f ( h ) ...
Page 1908
... Finite dimensional function on a group , definition , XI.1.3 ( 940 ) Finite dimensional spaces , additional properties , IV.15 ( 374 ) definitions , IV.2.1-8 ( 238-239 ) study of , IV.3 Finite intersection property , as crite- rion for ...
... Finite dimensional function on a group , definition , XI.1.3 ( 940 ) Finite dimensional spaces , additional properties , IV.15 ( 374 ) definitions , IV.2.1-8 ( 238-239 ) study of , IV.3 Finite intersection property , as crite- rion for ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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A₁ 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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero