Linear Operators, Part 2 |
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Page 866
... application of Zorn's lemma shows that this family contains a maxi- mal element . Thus any right ( and similarly for ... apply to right , left , or two - sided ideals . ( a ) An ideal contains no regular element . ( b ) The closure of an ...
... application of Zorn's lemma shows that this family contains a maxi- mal element . Thus any right ( and similarly for ... apply to right , left , or two - sided ideals . ( a ) An ideal contains no regular element . ( b ) The closure of an ...
Page 1612
... apply . The more general theory of spectral operators , to be developed in Chapters XV , XVI , XVII and XVIII will ... application of perturbation methods to self adjoint operators , and thus will , in the last analysis , lean upon the ...
... apply . The more general theory of spectral operators , to be developed in Chapters XV , XVI , XVII and XVIII will ... application of perturbation methods to self adjoint operators , and thus will , in the last analysis , lean upon the ...
Page 1618
... apply is ∞ lim -λ ( R ( -2 ; T ) f ) ( t ) = lim Σ 1400 λ λ → ∞ n = 1 2 + λn 이 cnfn ( t ) where 2 , is the nth eigenvalue . The limit exists for every square- integrable function f at all points t at which S® | f ( t + s ) —f ( t ) ...
... apply is ∞ lim -λ ( R ( -2 ; T ) f ) ( t ) = lim Σ 1400 λ λ → ∞ n = 1 2 + λn 이 cnfn ( t ) where 2 , is the nth eigenvalue . The limit exists for every square- integrable function f at all points t at which S® | f ( t + s ) —f ( t ) ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant 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 subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero